- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(and(true,X)) -> mark(X) [2] active(and(false,Y)) -> mark(false) [3] active(if(true,X,Y)) -> mark(X) [4] active(if(false,X,Y)) -> mark(Y) [5] active(add(0,X)) -> mark(X) [6] active(add(s(X),Y)) -> mark(s(add(X,Y))) [7] active(first(0,X)) -> mark(nil) [8] active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) [9] active(from(X)) -> mark(cons(X,from(s(X)))) [10] mark(and(X1,X2)) -> active(and(mark(X1),X2)) [11] mark(true) -> active(true) [12] mark(false) -> active(false) [13] mark(if(X1,X2,X3)) -> active(if(mark(X1),X2,X3)) [14] mark(add(X1,X2)) -> active(add(mark(X1),X2)) [15] mark(0) -> active(0) [16] mark(s(X)) -> active(s(X)) [17] mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) [18] mark(nil) -> active(nil) [19] mark(cons(X1,X2)) -> active(cons(X1,X2)) [20] mark(from(X)) -> active(from(X)) [21] and(mark(X1),X2) -> and(X1,X2) [22] and(X1,mark(X2)) -> and(X1,X2) [23] and(active(X1),X2) -> and(X1,X2) [24] and(X1,active(X2)) -> and(X1,X2) [25] if(mark(X1),X2,X3) -> if(X1,X2,X3) [26] if(X1,mark(X2),X3) -> if(X1,X2,X3) [27] if(X1,X2,mark(X3)) -> if(X1,X2,X3) [28] if(active(X1),X2,X3) -> if(X1,X2,X3) [29] if(X1,active(X2),X3) -> if(X1,X2,X3) [30] if(X1,X2,active(X3)) -> if(X1,X2,X3) [31] add(mark(X1),X2) -> add(X1,X2) [32] add(X1,mark(X2)) -> add(X1,X2) [33] add(active(X1),X2) -> add(X1,X2) [34] add(X1,active(X2)) -> add(X1,X2) [35] s(mark(X)) -> s(X) [36] s(active(X)) -> s(X) [37] first(mark(X1),X2) -> first(X1,X2) [38] first(X1,mark(X2)) -> first(X1,X2) [39] first(active(X1),X2) -> first(X1,X2) [40] first(X1,active(X2)) -> first(X1,X2) [41] cons(mark(X1),X2) -> cons(X1,X2) [42] cons(X1,mark(X2)) -> cons(X1,X2) [43] cons(active(X1),X2) -> cons(X1,X2) [44] cons(X1,active(X2)) -> cons(X1,X2) [45] from(mark(X)) -> from(X) [46] from(active(X)) -> from(X) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 8 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(true) >= active(true) ; mark(false) >= active(false) ; mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) ; mark(add(X1,X2)) >= active(add(mark(X1),X2)) ; mark(0) >= active(0) ; mark(s(X)) >= active(s(X)) ; mark(nil) >= active(nil) ; mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) ; mark(cons(X1,X2)) >= active(cons(X1,X2)) ; mark(from(X)) >= active(from(X)) ; active(and(true,X)) >= mark(X) ; active(and(false,Y)) >= mark(false) ; active(if(true,X,Y)) >= mark(X) ; active(if(false,X,Y)) >= mark(Y) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(first(0,X)) >= mark(nil) ; active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; if(mark(X1),X2,X3) >= if(X1,X2,X3) ; if(active(X1),X2,X3) >= if(X1,X2,X3) ; if(X1,mark(X2),X3) >= if(X1,X2,X3) ; if(X1,active(X2),X3) >= if(X1,X2,X3) ; if(X1,X2,mark(X3)) >= if(X1,X2,X3) ; if(X1,X2,active(X3)) >= if(X1,X2,X3) ; add(mark(X1),X2) >= add(X1,X2) ; add(active(X1),X2) >= add(X1,X2) ; add(X1,mark(X2)) >= add(X1,X2) ; add(X1,active(X2)) >= add(X1,X2) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; first(mark(X1),X2) >= first(X1,X2) ; first(active(X1),X2) >= first(X1,X2) ; first(X1,mark(X2)) >= first(X1,X2) ; first(X1,active(X2)) >= first(X1,X2) ; cons(mark(X1),X2) >= cons(X1,X2) ; cons(active(X1),X2) >= cons(X1,X2) ; cons(X1,mark(X2)) >= cons(X1,X2) ; cons(X1,active(X2)) >= cons(X1,X2) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) ; Marked_mark(add(X1,X2)) >= Marked_mark(X1) ; Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) ; Marked_mark(s(X)) >= Marked_active(s(X)) ; Marked_mark(first(X1,X2)) >= Marked_mark(X1) ; Marked_mark(first(X1,X2)) >= Marked_mark(X2) ; Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) ; Marked_mark(cons(X1,X2)) >= Marked_active(cons(X1,X2)) ; Marked_mark(from(X)) >= Marked_active(from(X)) ; Marked_active(and(true,X)) >= Marked_mark(X) ; Marked_active(if(true,X,Y)) >= Marked_mark(X) ; Marked_active(if(false,X,Y)) >= Marked_mark(Y) ; Marked_active(add(0,X)) >= Marked_mark(X) ; Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) ; Marked_active(first(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,first(X,Z))) ; Marked_active(from(X)) >= Marked_mark(cons(X,from(s(X)))) ; } + Disjunctions:{ { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(if(X1,X2,X3)) > Marked_active(if(mark(X1),X2,X3)) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(add(X1,X2)) > Marked_active(add(mark(X1),X2)) ; } { Marked_mark(s(X)) > Marked_active(s(X)) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(first(X1,X2)) > Marked_active(first(mark(X1),mark(X2))) ; } { Marked_mark(cons(X1,X2)) > Marked_active(cons(X1,X2)) ; } { Marked_mark(from(X)) > Marked_active(from(X)) ; } { Marked_active(and(true,X)) > Marked_mark(X) ; } { Marked_active(if(true,X,Y)) > Marked_mark(X) ; } { Marked_active(if(false,X,Y)) > Marked_mark(Y) ; } { Marked_active(add(0,X)) > Marked_mark(X) ; } { Marked_active(add(s(X),Y)) > Marked_mark(s(add(X,Y))) ; } { Marked_active(first(s(X),cons(Y,Z))) > Marked_mark(cons(Y,first(X,Z))) ; } { Marked_active(from(X)) > Marked_mark(cons(X,from(s(X)))) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(true) >= active(true) constraint: mark(false) >= active(false) constraint: mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) constraint: mark(add(X1,X2)) >= active(add(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(s(X)) >= active(s(X)) constraint: mark(nil) >= active(nil) constraint: mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) constraint: mark(cons(X1,X2)) >= active(cons(X1,X2)) constraint: mark(from(X)) >= active(from(X)) constraint: active(and(true,X)) >= mark(X) constraint: active(and(false,Y)) >= mark(false) constraint: active(if(true,X,Y)) >= mark(X) constraint: active(if(false,X,Y)) >= mark(Y) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(first(0,X)) >= mark(nil) constraint: active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: if(mark(X1),X2,X3) >= if(X1,X2,X3) constraint: if(active(X1),X2,X3) >= if(X1,X2,X3) constraint: if(X1,mark(X2),X3) >= if(X1,X2,X3) constraint: if(X1,active(X2),X3) >= if(X1,X2,X3) constraint: if(X1,X2,mark(X3)) >= if(X1,X2,X3) constraint: if(X1,X2,active(X3)) >= if(X1,X2,X3) constraint: add(mark(X1),X2) >= add(X1,X2) constraint: add(active(X1),X2) >= add(X1,X2) constraint: add(X1,mark(X2)) >= add(X1,X2) constraint: add(X1,active(X2)) >= add(X1,X2) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: first(mark(X1),X2) >= first(X1,X2) constraint: first(active(X1),X2) >= first(X1,X2) constraint: first(X1,mark(X2)) >= first(X1,X2) constraint: first(X1,active(X2)) >= first(X1,X2) constraint: cons(mark(X1),X2) >= cons(X1,X2) constraint: cons(active(X1),X2) >= cons(X1,X2) constraint: cons(X1,mark(X2)) >= cons(X1,X2) constraint: cons(X1,active(X2)) >= cons(X1,X2) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) constraint: Marked_mark(s(X)) >= Marked_active(s(X)) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) constraint: Marked_mark(cons(X1,X2)) >= Marked_active(cons(X1,X2)) constraint: Marked_mark(from(X)) >= Marked_active(from(X)) constraint: Marked_active(and(true,X)) >= Marked_mark(X) constraint: Marked_active(if(true,X,Y)) >= Marked_mark(X) constraint: Marked_active(if(false,X,Y)) >= Marked_mark(Y) constraint: Marked_active(add(0,X)) >= Marked_mark(X) constraint: Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) constraint: Marked_active(first(s(X),cons(Y,Z))) >= Marked_mark(cons( Y,first(X,Z))) constraint: Marked_active(from(X)) >= Marked_mark(cons(X,from(s(X)))) APPLY CRITERIA (Subterm criterion) ST: Marked_and -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_if -> 3 APPLY CRITERIA (Subterm criterion) ST: Marked_add -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_s -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_first -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_cons -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_from -> 1 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(true) >= active(true) ; mark(false) >= active(false) ; mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) ; mark(add(X1,X2)) >= active(add(mark(X1),X2)) ; mark(0) >= active(0) ; mark(s(X)) >= active(s(X)) ; mark(nil) >= active(nil) ; mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) ; mark(cons(X1,X2)) >= active(cons(X1,X2)) ; mark(from(X)) >= active(from(X)) ; active(and(true,X)) >= mark(X) ; active(and(false,Y)) >= mark(false) ; active(if(true,X,Y)) >= mark(X) ; active(if(false,X,Y)) >= mark(Y) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(first(0,X)) >= mark(nil) ; active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; if(mark(X1),X2,X3) >= if(X1,X2,X3) ; if(active(X1),X2,X3) >= if(X1,X2,X3) ; if(X1,mark(X2),X3) >= if(X1,X2,X3) ; if(X1,active(X2),X3) >= if(X1,X2,X3) ; if(X1,X2,mark(X3)) >= if(X1,X2,X3) ; if(X1,X2,active(X3)) >= if(X1,X2,X3) ; add(mark(X1),X2) >= add(X1,X2) ; add(active(X1),X2) >= add(X1,X2) ; add(X1,mark(X2)) >= add(X1,X2) ; add(X1,active(X2)) >= add(X1,X2) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; first(mark(X1),X2) >= first(X1,X2) ; first(active(X1),X2) >= first(X1,X2) ; first(X1,mark(X2)) >= first(X1,X2) ; first(X1,active(X2)) >= first(X1,X2) ; cons(mark(X1),X2) >= cons(X1,X2) ; cons(active(X1),X2) >= cons(X1,X2) ; cons(X1,mark(X2)) >= cons(X1,X2) ; cons(X1,active(X2)) >= cons(X1,X2) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) ; Marked_mark(add(X1,X2)) >= Marked_mark(X1) ; Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) ; Marked_mark(s(X)) >= Marked_active(s(X)) ; Marked_mark(first(X1,X2)) >= Marked_mark(X1) ; Marked_mark(first(X1,X2)) >= Marked_mark(X2) ; Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) ; Marked_mark(cons(X1,X2)) >= Marked_active(cons(X1,X2)) ; Marked_mark(from(X)) >= Marked_active(from(X)) ; Marked_active(and(true,X)) >= Marked_mark(X) ; Marked_active(if(true,X,Y)) >= Marked_mark(X) ; Marked_active(add(0,X)) >= Marked_mark(X) ; Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) ; Marked_active(first(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,first(X,Z))) ; Marked_active(from(X)) >= Marked_mark(cons(X,from(s(X)))) ; } + Disjunctions:{ { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(if(X1,X2,X3)) > Marked_active(if(mark(X1),X2,X3)) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(add(X1,X2)) > Marked_active(add(mark(X1),X2)) ; } { Marked_mark(s(X)) > Marked_active(s(X)) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(first(X1,X2)) > Marked_active(first(mark(X1),mark(X2))) ; } { Marked_mark(cons(X1,X2)) > Marked_active(cons(X1,X2)) ; } { Marked_mark(from(X)) > Marked_active(from(X)) ; } { Marked_active(and(true,X)) > Marked_mark(X) ; } { Marked_active(if(true,X,Y)) > Marked_mark(X) ; } { Marked_active(add(0,X)) > Marked_mark(X) ; } { Marked_active(add(s(X),Y)) > Marked_mark(s(add(X,Y))) ; } { Marked_active(first(s(X),cons(Y,Z))) > Marked_mark(cons(Y,first(X,Z))) ; } { Marked_active(from(X)) > Marked_mark(cons(X,from(s(X)))) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(true) >= active(true) constraint: mark(false) >= active(false) constraint: mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) constraint: mark(add(X1,X2)) >= active(add(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(s(X)) >= active(s(X)) constraint: mark(nil) >= active(nil) constraint: mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) constraint: mark(cons(X1,X2)) >= active(cons(X1,X2)) constraint: mark(from(X)) >= active(from(X)) constraint: active(and(true,X)) >= mark(X) constraint: active(and(false,Y)) >= mark(false) constraint: active(if(true,X,Y)) >= mark(X) constraint: active(if(false,X,Y)) >= mark(Y) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(first(0,X)) >= mark(nil) constraint: active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: if(mark(X1),X2,X3) >= if(X1,X2,X3) constraint: if(active(X1),X2,X3) >= if(X1,X2,X3) constraint: if(X1,mark(X2),X3) >= if(X1,X2,X3) constraint: if(X1,active(X2),X3) >= if(X1,X2,X3) constraint: if(X1,X2,mark(X3)) >= if(X1,X2,X3) constraint: if(X1,X2,active(X3)) >= if(X1,X2,X3) constraint: add(mark(X1),X2) >= add(X1,X2) constraint: add(active(X1),X2) >= add(X1,X2) constraint: add(X1,mark(X2)) >= add(X1,X2) constraint: add(X1,active(X2)) >= add(X1,X2) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: first(mark(X1),X2) >= first(X1,X2) constraint: first(active(X1),X2) >= first(X1,X2) constraint: first(X1,mark(X2)) >= first(X1,X2) constraint: first(X1,active(X2)) >= first(X1,X2) constraint: cons(mark(X1),X2) >= cons(X1,X2) constraint: cons(active(X1),X2) >= cons(X1,X2) constraint: cons(X1,mark(X2)) >= cons(X1,X2) constraint: cons(X1,active(X2)) >= cons(X1,X2) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) constraint: Marked_mark(s(X)) >= Marked_active(s(X)) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) constraint: Marked_mark(cons(X1,X2)) >= Marked_active(cons(X1,X2)) constraint: Marked_mark(from(X)) >= Marked_active(from(X)) constraint: Marked_active(and(true,X)) >= Marked_mark(X) constraint: Marked_active(if(true,X,Y)) >= Marked_mark(X) constraint: Marked_active(add(0,X)) >= Marked_mark(X) constraint: Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) constraint: Marked_active(first(s(X),cons(Y,Z))) >= Marked_mark(cons( Y,first(X,Z))) constraint: Marked_active(from(X)) >= Marked_mark(cons(X,from(s(X)))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(true) >= active(true) ; mark(false) >= active(false) ; mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) ; mark(add(X1,X2)) >= active(add(mark(X1),X2)) ; mark(0) >= active(0) ; mark(s(X)) >= active(s(X)) ; mark(nil) >= active(nil) ; mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) ; mark(cons(X1,X2)) >= active(cons(X1,X2)) ; mark(from(X)) >= active(from(X)) ; active(and(true,X)) >= mark(X) ; active(and(false,Y)) >= mark(false) ; active(if(true,X,Y)) >= mark(X) ; active(if(false,X,Y)) >= mark(Y) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(first(0,X)) >= mark(nil) ; active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; if(mark(X1),X2,X3) >= if(X1,X2,X3) ; if(active(X1),X2,X3) >= if(X1,X2,X3) ; if(X1,mark(X2),X3) >= if(X1,X2,X3) ; if(X1,active(X2),X3) >= if(X1,X2,X3) ; if(X1,X2,mark(X3)) >= if(X1,X2,X3) ; if(X1,X2,active(X3)) >= if(X1,X2,X3) ; add(mark(X1),X2) >= add(X1,X2) ; add(active(X1),X2) >= add(X1,X2) ; add(X1,mark(X2)) >= add(X1,X2) ; add(X1,active(X2)) >= add(X1,X2) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; first(mark(X1),X2) >= first(X1,X2) ; first(active(X1),X2) >= first(X1,X2) ; first(X1,mark(X2)) >= first(X1,X2) ; first(X1,active(X2)) >= first(X1,X2) ; cons(mark(X1),X2) >= cons(X1,X2) ; cons(active(X1),X2) >= cons(X1,X2) ; cons(X1,mark(X2)) >= cons(X1,X2) ; cons(X1,active(X2)) >= cons(X1,X2) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) ; Marked_mark(add(X1,X2)) >= Marked_mark(X1) ; Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) ; Marked_mark(s(X)) >= Marked_active(s(X)) ; Marked_mark(first(X1,X2)) >= Marked_mark(X1) ; Marked_mark(first(X1,X2)) >= Marked_mark(X2) ; Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) ; Marked_mark(cons(X1,X2)) >= Marked_active(cons(X1,X2)) ; Marked_mark(from(X)) >= Marked_active(from(X)) ; Marked_active(and(true,X)) >= Marked_mark(X) ; Marked_active(if(true,X,Y)) >= Marked_mark(X) ; Marked_active(add(0,X)) >= Marked_mark(X) ; Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) ; Marked_active(first(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,first(X,Z))) ; } + Disjunctions:{ { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(if(X1,X2,X3)) > Marked_active(if(mark(X1),X2,X3)) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(add(X1,X2)) > Marked_active(add(mark(X1),X2)) ; } { Marked_mark(s(X)) > Marked_active(s(X)) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(first(X1,X2)) > Marked_active(first(mark(X1),mark(X2))) ; } { Marked_mark(cons(X1,X2)) > Marked_active(cons(X1,X2)) ; } { Marked_mark(from(X)) > Marked_active(from(X)) ; } { Marked_active(and(true,X)) > Marked_mark(X) ; } { Marked_active(if(true,X,Y)) > Marked_mark(X) ; } { Marked_active(add(0,X)) > Marked_mark(X) ; } { Marked_active(add(s(X),Y)) > Marked_mark(s(add(X,Y))) ; } { Marked_active(first(s(X),cons(Y,Z))) > Marked_mark(cons(Y,first(X,Z))) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(true) >= active(true) constraint: mark(false) >= active(false) constraint: mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) constraint: mark(add(X1,X2)) >= active(add(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(s(X)) >= active(s(X)) constraint: mark(nil) >= active(nil) constraint: mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) constraint: mark(cons(X1,X2)) >= active(cons(X1,X2)) constraint: mark(from(X)) >= active(from(X)) constraint: active(and(true,X)) >= mark(X) constraint: active(and(false,Y)) >= mark(false) constraint: active(if(true,X,Y)) >= mark(X) constraint: active(if(false,X,Y)) >= mark(Y) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(first(0,X)) >= mark(nil) constraint: active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: if(mark(X1),X2,X3) >= if(X1,X2,X3) constraint: if(active(X1),X2,X3) >= if(X1,X2,X3) constraint: if(X1,mark(X2),X3) >= if(X1,X2,X3) constraint: if(X1,active(X2),X3) >= if(X1,X2,X3) constraint: if(X1,X2,mark(X3)) >= if(X1,X2,X3) constraint: if(X1,X2,active(X3)) >= if(X1,X2,X3) constraint: add(mark(X1),X2) >= add(X1,X2) constraint: add(active(X1),X2) >= add(X1,X2) constraint: add(X1,mark(X2)) >= add(X1,X2) constraint: add(X1,active(X2)) >= add(X1,X2) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: first(mark(X1),X2) >= first(X1,X2) constraint: first(active(X1),X2) >= first(X1,X2) constraint: first(X1,mark(X2)) >= first(X1,X2) constraint: first(X1,active(X2)) >= first(X1,X2) constraint: cons(mark(X1),X2) >= cons(X1,X2) constraint: cons(active(X1),X2) >= cons(X1,X2) constraint: cons(X1,mark(X2)) >= cons(X1,X2) constraint: cons(X1,active(X2)) >= cons(X1,X2) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) constraint: Marked_mark(s(X)) >= Marked_active(s(X)) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) constraint: Marked_mark(cons(X1,X2)) >= Marked_active(cons(X1,X2)) constraint: Marked_mark(from(X)) >= Marked_active(from(X)) constraint: Marked_active(and(true,X)) >= Marked_mark(X) constraint: Marked_active(if(true,X,Y)) >= Marked_mark(X) constraint: Marked_active(add(0,X)) >= Marked_mark(X) constraint: Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) constraint: Marked_active(first(s(X),cons(Y,Z))) >= Marked_mark(cons( Y,first(X,Z))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(true) >= active(true) ; mark(false) >= active(false) ; mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) ; mark(add(X1,X2)) >= active(add(mark(X1),X2)) ; mark(0) >= active(0) ; mark(s(X)) >= active(s(X)) ; mark(nil) >= active(nil) ; mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) ; mark(cons(X1,X2)) >= active(cons(X1,X2)) ; mark(from(X)) >= active(from(X)) ; active(and(true,X)) >= mark(X) ; active(and(false,Y)) >= mark(false) ; active(if(true,X,Y)) >= mark(X) ; active(if(false,X,Y)) >= mark(Y) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(first(0,X)) >= mark(nil) ; active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; if(mark(X1),X2,X3) >= if(X1,X2,X3) ; if(active(X1),X2,X3) >= if(X1,X2,X3) ; if(X1,mark(X2),X3) >= if(X1,X2,X3) ; if(X1,active(X2),X3) >= if(X1,X2,X3) ; if(X1,X2,mark(X3)) >= if(X1,X2,X3) ; if(X1,X2,active(X3)) >= if(X1,X2,X3) ; add(mark(X1),X2) >= add(X1,X2) ; add(active(X1),X2) >= add(X1,X2) ; add(X1,mark(X2)) >= add(X1,X2) ; add(X1,active(X2)) >= add(X1,X2) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; first(mark(X1),X2) >= first(X1,X2) ; first(active(X1),X2) >= first(X1,X2) ; first(X1,mark(X2)) >= first(X1,X2) ; first(X1,active(X2)) >= first(X1,X2) ; cons(mark(X1),X2) >= cons(X1,X2) ; cons(active(X1),X2) >= cons(X1,X2) ; cons(X1,mark(X2)) >= cons(X1,X2) ; cons(X1,active(X2)) >= cons(X1,X2) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) ; Marked_mark(add(X1,X2)) >= Marked_mark(X1) ; Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) ; Marked_mark(s(X)) >= Marked_active(s(X)) ; Marked_mark(first(X1,X2)) >= Marked_mark(X1) ; Marked_mark(first(X1,X2)) >= Marked_mark(X2) ; Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) ; Marked_mark(cons(X1,X2)) >= Marked_active(cons(X1,X2)) ; Marked_mark(from(X)) >= Marked_active(from(X)) ; Marked_active(and(true,X)) >= Marked_mark(X) ; Marked_active(if(true,X,Y)) >= Marked_mark(X) ; Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) ; Marked_active(first(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,first(X,Z))) ; } + Disjunctions:{ { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(if(X1,X2,X3)) > Marked_active(if(mark(X1),X2,X3)) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(add(X1,X2)) > Marked_active(add(mark(X1),X2)) ; } { Marked_mark(s(X)) > Marked_active(s(X)) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(first(X1,X2)) > Marked_active(first(mark(X1),mark(X2))) ; } { Marked_mark(cons(X1,X2)) > Marked_active(cons(X1,X2)) ; } { Marked_mark(from(X)) > Marked_active(from(X)) ; } { Marked_active(and(true,X)) > Marked_mark(X) ; } { Marked_active(if(true,X,Y)) > Marked_mark(X) ; } { Marked_active(add(s(X),Y)) > Marked_mark(s(add(X,Y))) ; } { Marked_active(first(s(X),cons(Y,Z))) > Marked_mark(cons(Y,first(X,Z))) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(true) >= active(true) constraint: mark(false) >= active(false) constraint: mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) constraint: mark(add(X1,X2)) >= active(add(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(s(X)) >= active(s(X)) constraint: mark(nil) >= active(nil) constraint: mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) constraint: mark(cons(X1,X2)) >= active(cons(X1,X2)) constraint: mark(from(X)) >= active(from(X)) constraint: active(and(true,X)) >= mark(X) constraint: active(and(false,Y)) >= mark(false) constraint: active(if(true,X,Y)) >= mark(X) constraint: active(if(false,X,Y)) >= mark(Y) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(first(0,X)) >= mark(nil) constraint: active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: if(mark(X1),X2,X3) >= if(X1,X2,X3) constraint: if(active(X1),X2,X3) >= if(X1,X2,X3) constraint: if(X1,mark(X2),X3) >= if(X1,X2,X3) constraint: if(X1,active(X2),X3) >= if(X1,X2,X3) constraint: if(X1,X2,mark(X3)) >= if(X1,X2,X3) constraint: if(X1,X2,active(X3)) >= if(X1,X2,X3) constraint: add(mark(X1),X2) >= add(X1,X2) constraint: add(active(X1),X2) >= add(X1,X2) constraint: add(X1,mark(X2)) >= add(X1,X2) constraint: add(X1,active(X2)) >= add(X1,X2) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: first(mark(X1),X2) >= first(X1,X2) constraint: first(active(X1),X2) >= first(X1,X2) constraint: first(X1,mark(X2)) >= first(X1,X2) constraint: first(X1,active(X2)) >= first(X1,X2) constraint: cons(mark(X1),X2) >= cons(X1,X2) constraint: cons(active(X1),X2) >= cons(X1,X2) constraint: cons(X1,mark(X2)) >= cons(X1,X2) constraint: cons(X1,active(X2)) >= cons(X1,X2) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) constraint: Marked_mark(s(X)) >= Marked_active(s(X)) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) constraint: Marked_mark(cons(X1,X2)) >= Marked_active(cons(X1,X2)) constraint: Marked_mark(from(X)) >= Marked_active(from(X)) constraint: Marked_active(and(true,X)) >= Marked_mark(X) constraint: Marked_active(if(true,X,Y)) >= Marked_mark(X) constraint: Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) constraint: Marked_active(first(s(X),cons(Y,Z))) >= Marked_mark(cons( Y,first(X,Z))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(true) >= active(true) ; mark(false) >= active(false) ; mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) ; mark(add(X1,X2)) >= active(add(mark(X1),X2)) ; mark(0) >= active(0) ; mark(s(X)) >= active(s(X)) ; mark(nil) >= active(nil) ; mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) ; mark(cons(X1,X2)) >= active(cons(X1,X2)) ; mark(from(X)) >= active(from(X)) ; active(and(true,X)) >= mark(X) ; active(and(false,Y)) >= mark(false) ; active(if(true,X,Y)) >= mark(X) ; active(if(false,X,Y)) >= mark(Y) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(first(0,X)) >= mark(nil) ; active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; if(mark(X1),X2,X3) >= if(X1,X2,X3) ; if(active(X1),X2,X3) >= if(X1,X2,X3) ; if(X1,mark(X2),X3) >= if(X1,X2,X3) ; if(X1,active(X2),X3) >= if(X1,X2,X3) ; if(X1,X2,mark(X3)) >= if(X1,X2,X3) ; if(X1,X2,active(X3)) >= if(X1,X2,X3) ; add(mark(X1),X2) >= add(X1,X2) ; add(active(X1),X2) >= add(X1,X2) ; add(X1,mark(X2)) >= add(X1,X2) ; add(X1,active(X2)) >= add(X1,X2) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; first(mark(X1),X2) >= first(X1,X2) ; first(active(X1),X2) >= first(X1,X2) ; first(X1,mark(X2)) >= first(X1,X2) ; first(X1,active(X2)) >= first(X1,X2) ; cons(mark(X1),X2) >= cons(X1,X2) ; cons(active(X1),X2) >= cons(X1,X2) ; cons(X1,mark(X2)) >= cons(X1,X2) ; cons(X1,active(X2)) >= cons(X1,X2) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) ; Marked_mark(add(X1,X2)) >= Marked_mark(X1) ; Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) ; Marked_mark(first(X1,X2)) >= Marked_mark(X1) ; Marked_mark(first(X1,X2)) >= Marked_mark(X2) ; Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) ; Marked_active(and(true,X)) >= Marked_mark(X) ; Marked_active(if(true,X,Y)) >= Marked_mark(X) ; Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) ; Marked_active(first(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,first(X,Z))) ; } + Disjunctions:{ { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(if(X1,X2,X3)) > Marked_active(if(mark(X1),X2,X3)) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(add(X1,X2)) > Marked_active(add(mark(X1),X2)) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(first(X1,X2)) > Marked_active(first(mark(X1),mark(X2))) ; } { Marked_active(and(true,X)) > Marked_mark(X) ; } { Marked_active(if(true,X,Y)) > Marked_mark(X) ; } { Marked_active(add(s(X),Y)) > Marked_mark(s(add(X,Y))) ; } { Marked_active(first(s(X),cons(Y,Z))) > Marked_mark(cons(Y,first(X,Z))) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(true) >= active(true) constraint: mark(false) >= active(false) constraint: mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) constraint: mark(add(X1,X2)) >= active(add(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(s(X)) >= active(s(X)) constraint: mark(nil) >= active(nil) constraint: mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) constraint: mark(cons(X1,X2)) >= active(cons(X1,X2)) constraint: mark(from(X)) >= active(from(X)) constraint: active(and(true,X)) >= mark(X) constraint: active(and(false,Y)) >= mark(false) constraint: active(if(true,X,Y)) >= mark(X) constraint: active(if(false,X,Y)) >= mark(Y) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(first(0,X)) >= mark(nil) constraint: active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: if(mark(X1),X2,X3) >= if(X1,X2,X3) constraint: if(active(X1),X2,X3) >= if(X1,X2,X3) constraint: if(X1,mark(X2),X3) >= if(X1,X2,X3) constraint: if(X1,active(X2),X3) >= if(X1,X2,X3) constraint: if(X1,X2,mark(X3)) >= if(X1,X2,X3) constraint: if(X1,X2,active(X3)) >= if(X1,X2,X3) constraint: add(mark(X1),X2) >= add(X1,X2) constraint: add(active(X1),X2) >= add(X1,X2) constraint: add(X1,mark(X2)) >= add(X1,X2) constraint: add(X1,active(X2)) >= add(X1,X2) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: first(mark(X1),X2) >= first(X1,X2) constraint: first(active(X1),X2) >= first(X1,X2) constraint: first(X1,mark(X2)) >= first(X1,X2) constraint: first(X1,active(X2)) >= first(X1,X2) constraint: cons(mark(X1),X2) >= cons(X1,X2) constraint: cons(active(X1),X2) >= cons(X1,X2) constraint: cons(X1,mark(X2)) >= cons(X1,X2) constraint: cons(X1,active(X2)) >= cons(X1,X2) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) constraint: Marked_active(and(true,X)) >= Marked_mark(X) constraint: Marked_active(if(true,X,Y)) >= Marked_mark(X) constraint: Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) constraint: Marked_active(first(s(X),cons(Y,Z))) >= Marked_mark(cons( Y,first(X,Z))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(true) >= active(true) ; mark(false) >= active(false) ; mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) ; mark(add(X1,X2)) >= active(add(mark(X1),X2)) ; mark(0) >= active(0) ; mark(s(X)) >= active(s(X)) ; mark(nil) >= active(nil) ; mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) ; mark(cons(X1,X2)) >= active(cons(X1,X2)) ; mark(from(X)) >= active(from(X)) ; active(and(true,X)) >= mark(X) ; active(and(false,Y)) >= mark(false) ; active(if(true,X,Y)) >= mark(X) ; active(if(false,X,Y)) >= mark(Y) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(first(0,X)) >= mark(nil) ; active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; if(mark(X1),X2,X3) >= if(X1,X2,X3) ; if(active(X1),X2,X3) >= if(X1,X2,X3) ; if(X1,mark(X2),X3) >= if(X1,X2,X3) ; if(X1,active(X2),X3) >= if(X1,X2,X3) ; if(X1,X2,mark(X3)) >= if(X1,X2,X3) ; if(X1,X2,active(X3)) >= if(X1,X2,X3) ; add(mark(X1),X2) >= add(X1,X2) ; add(active(X1),X2) >= add(X1,X2) ; add(X1,mark(X2)) >= add(X1,X2) ; add(X1,active(X2)) >= add(X1,X2) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; first(mark(X1),X2) >= first(X1,X2) ; first(active(X1),X2) >= first(X1,X2) ; first(X1,mark(X2)) >= first(X1,X2) ; first(X1,active(X2)) >= first(X1,X2) ; cons(mark(X1),X2) >= cons(X1,X2) ; cons(active(X1),X2) >= cons(X1,X2) ; cons(X1,mark(X2)) >= cons(X1,X2) ; cons(X1,active(X2)) >= cons(X1,X2) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) ; Marked_mark(add(X1,X2)) >= Marked_mark(X1) ; Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) ; Marked_mark(first(X1,X2)) >= Marked_mark(X1) ; Marked_mark(first(X1,X2)) >= Marked_mark(X2) ; Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) ; Marked_active(and(true,X)) >= Marked_mark(X) ; Marked_active(if(true,X,Y)) >= Marked_mark(X) ; Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) ; } + Disjunctions:{ { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(if(X1,X2,X3)) > Marked_active(if(mark(X1),X2,X3)) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(add(X1,X2)) > Marked_active(add(mark(X1),X2)) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(first(X1,X2)) > Marked_active(first(mark(X1),mark(X2))) ; } { Marked_active(and(true,X)) > Marked_mark(X) ; } { Marked_active(if(true,X,Y)) > Marked_mark(X) ; } { Marked_active(add(s(X),Y)) > Marked_mark(s(add(X,Y))) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(true) >= active(true) constraint: mark(false) >= active(false) constraint: mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) constraint: mark(add(X1,X2)) >= active(add(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(s(X)) >= active(s(X)) constraint: mark(nil) >= active(nil) constraint: mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) constraint: mark(cons(X1,X2)) >= active(cons(X1,X2)) constraint: mark(from(X)) >= active(from(X)) constraint: active(and(true,X)) >= mark(X) constraint: active(and(false,Y)) >= mark(false) constraint: active(if(true,X,Y)) >= mark(X) constraint: active(if(false,X,Y)) >= mark(Y) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(first(0,X)) >= mark(nil) constraint: active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: if(mark(X1),X2,X3) >= if(X1,X2,X3) constraint: if(active(X1),X2,X3) >= if(X1,X2,X3) constraint: if(X1,mark(X2),X3) >= if(X1,X2,X3) constraint: if(X1,active(X2),X3) >= if(X1,X2,X3) constraint: if(X1,X2,mark(X3)) >= if(X1,X2,X3) constraint: if(X1,X2,active(X3)) >= if(X1,X2,X3) constraint: add(mark(X1),X2) >= add(X1,X2) constraint: add(active(X1),X2) >= add(X1,X2) constraint: add(X1,mark(X2)) >= add(X1,X2) constraint: add(X1,active(X2)) >= add(X1,X2) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: first(mark(X1),X2) >= first(X1,X2) constraint: first(active(X1),X2) >= first(X1,X2) constraint: first(X1,mark(X2)) >= first(X1,X2) constraint: first(X1,active(X2)) >= first(X1,X2) constraint: cons(mark(X1),X2) >= cons(X1,X2) constraint: cons(active(X1),X2) >= cons(X1,X2) constraint: cons(X1,mark(X2)) >= cons(X1,X2) constraint: cons(X1,active(X2)) >= cons(X1,X2) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) constraint: Marked_active(and(true,X)) >= Marked_mark(X) constraint: Marked_active(if(true,X,Y)) >= Marked_mark(X) constraint: Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(and(X1,X2)) >= active(and(mark(X1),X2)) ; mark(true) >= active(true) ; mark(false) >= active(false) ; mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) ; mark(add(X1,X2)) >= active(add(mark(X1),X2)) ; mark(0) >= active(0) ; mark(s(X)) >= active(s(X)) ; mark(nil) >= active(nil) ; mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) ; mark(cons(X1,X2)) >= active(cons(X1,X2)) ; mark(from(X)) >= active(from(X)) ; active(and(true,X)) >= mark(X) ; active(and(false,Y)) >= mark(false) ; active(if(true,X,Y)) >= mark(X) ; active(if(false,X,Y)) >= mark(Y) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(first(0,X)) >= mark(nil) ; active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; and(mark(X1),X2) >= and(X1,X2) ; and(active(X1),X2) >= and(X1,X2) ; and(X1,mark(X2)) >= and(X1,X2) ; and(X1,active(X2)) >= and(X1,X2) ; if(mark(X1),X2,X3) >= if(X1,X2,X3) ; if(active(X1),X2,X3) >= if(X1,X2,X3) ; if(X1,mark(X2),X3) >= if(X1,X2,X3) ; if(X1,active(X2),X3) >= if(X1,X2,X3) ; if(X1,X2,mark(X3)) >= if(X1,X2,X3) ; if(X1,X2,active(X3)) >= if(X1,X2,X3) ; add(mark(X1),X2) >= add(X1,X2) ; add(active(X1),X2) >= add(X1,X2) ; add(X1,mark(X2)) >= add(X1,X2) ; add(X1,active(X2)) >= add(X1,X2) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; first(mark(X1),X2) >= first(X1,X2) ; first(active(X1),X2) >= first(X1,X2) ; first(X1,mark(X2)) >= first(X1,X2) ; first(X1,active(X2)) >= first(X1,X2) ; cons(mark(X1),X2) >= cons(X1,X2) ; cons(active(X1),X2) >= cons(X1,X2) ; cons(X1,mark(X2)) >= cons(X1,X2) ; cons(X1,active(X2)) >= cons(X1,X2) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; Marked_mark(and(X1,X2)) >= Marked_mark(X1) ; Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ; Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) ; Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) ; Marked_mark(first(X1,X2)) >= Marked_mark(X1) ; Marked_mark(first(X1,X2)) >= Marked_mark(X2) ; Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) ; Marked_active(and(true,X)) >= Marked_mark(X) ; Marked_active(if(true,X,Y)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_mark(and(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ; } { Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(if(X1,X2,X3)) > Marked_active(if(mark(X1),X2,X3)) ; } { Marked_mark(add(X1,X2)) > Marked_active(add(mark(X1),X2)) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(first(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(first(X1,X2)) > Marked_active(first(mark(X1),mark(X2))) ; } { Marked_active(and(true,X)) > Marked_mark(X) ; } { Marked_active(if(true,X,Y)) > Marked_mark(X) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2)) constraint: mark(true) >= active(true) constraint: mark(false) >= active(false) constraint: mark(if(X1,X2,X3)) >= active(if(mark(X1),X2,X3)) constraint: mark(add(X1,X2)) >= active(add(mark(X1),X2)) constraint: mark(0) >= active(0) constraint: mark(s(X)) >= active(s(X)) constraint: mark(nil) >= active(nil) constraint: mark(first(X1,X2)) >= active(first(mark(X1),mark(X2))) constraint: mark(cons(X1,X2)) >= active(cons(X1,X2)) constraint: mark(from(X)) >= active(from(X)) constraint: active(and(true,X)) >= mark(X) constraint: active(and(false,Y)) >= mark(false) constraint: active(if(true,X,Y)) >= mark(X) constraint: active(if(false,X,Y)) >= mark(Y) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(first(0,X)) >= mark(nil) constraint: active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: and(mark(X1),X2) >= and(X1,X2) constraint: and(active(X1),X2) >= and(X1,X2) constraint: and(X1,mark(X2)) >= and(X1,X2) constraint: and(X1,active(X2)) >= and(X1,X2) constraint: if(mark(X1),X2,X3) >= if(X1,X2,X3) constraint: if(active(X1),X2,X3) >= if(X1,X2,X3) constraint: if(X1,mark(X2),X3) >= if(X1,X2,X3) constraint: if(X1,active(X2),X3) >= if(X1,X2,X3) constraint: if(X1,X2,mark(X3)) >= if(X1,X2,X3) constraint: if(X1,X2,active(X3)) >= if(X1,X2,X3) constraint: add(mark(X1),X2) >= add(X1,X2) constraint: add(active(X1),X2) >= add(X1,X2) constraint: add(X1,mark(X2)) >= add(X1,X2) constraint: add(X1,active(X2)) >= add(X1,X2) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: first(mark(X1),X2) >= first(X1,X2) constraint: first(active(X1),X2) >= first(X1,X2) constraint: first(X1,mark(X2)) >= first(X1,X2) constraint: first(X1,active(X2)) >= first(X1,X2) constraint: cons(mark(X1),X2) >= cons(X1,X2) constraint: cons(active(X1),X2) >= cons(X1,X2) constraint: cons(X1,mark(X2)) >= cons(X1,X2) constraint: cons(X1,active(X2)) >= cons(X1,X2) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(if(X1,X2,X3)) >= Marked_active(if(mark(X1),X2,X3)) constraint: Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),X2)) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(first(X1,X2)) >= Marked_active(first(mark(X1),mark(X2))) constraint: Marked_active(and(true,X)) >= Marked_mark(X) constraint: Marked_active(if(true,X,Y)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_mark -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_and -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_if -> 2 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_if -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_add -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_first -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_cons -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] active(and(true,X)) -> mark(X) [2] active(and(false,Y)) -> mark(false) [3] active(if(true,X,Y)) -> mark(X) [4] active(if(false,X,Y)) -> mark(Y) [5] active(add(0,X)) -> mark(X) [6] active(add(s(X),Y)) -> mark(s(add(X,Y))) [7] active(first(0,X)) -> mark(nil) [8] active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) [9] active(from(X)) -> mark(cons(X,from(s(X)))) [10] mark(and(X1,X2)) -> active(and(mark(X1),X2)) [11] mark(true) -> active(true) [12] mark(false) -> active(false) [13] mark(if(X1,X2,X3)) -> active(if(mark(X1),X2,X3)) [14] mark(add(X1,X2)) -> active(add(mark(X1),X2)) [15] mark(0) -> active(0) [16] mark(s(X)) -> active(s(X)) [17] mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) [18] mark(nil) -> active(nil) [19] mark(cons(X1,X2)) -> active(cons(X1,X2)) [20] mark(from(X)) -> active(from(X)) [21] and(mark(X1),X2) -> and(X1,X2) [22] and(X1,mark(X2)) -> and(X1,X2) [23] and(active(X1),X2) -> and(X1,X2) [24] and(X1,active(X2)) -> and(X1,X2) [25] if(mark(X1),X2,X3) -> if(X1,X2,X3) [26] if(X1,mark(X2),X3) -> if(X1,X2,X3) [27] if(X1,X2,mark(X3)) -> if(X1,X2,X3) [28] if(active(X1),X2,X3) -> if(X1,X2,X3) [29] if(X1,active(X2),X3) -> if(X1,X2,X3) [30] if(X1,X2,active(X3)) -> if(X1,X2,X3) [31] add(mark(X1),X2) -> add(X1,X2) [32] add(X1,mark(X2)) -> add(X1,X2) [33] add(active(X1),X2) -> add(X1,X2) [34] add(X1,active(X2)) -> add(X1,X2) [35] s(mark(X)) -> s(X) [36] s(active(X)) -> s(X) [37] first(mark(X1),X2) -> first(X1,X2) [38] first(X1,mark(X2)) -> first(X1,X2) [39] first(active(X1),X2) -> first(X1,X2) [40] first(X1,active(X2)) -> first(X1,X2) [41] cons(mark(X1),X2) -> cons(X1,X2) [42] cons(X1,mark(X2)) -> cons(X1,X2) [43] cons(active(X1),X2) -> cons(X1,X2) [44] cons(X1,active(X2)) -> cons(X1,X2) [45] from(mark(X)) -> from(X) [46] from(active(X)) -> from(X) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 2*X0; [ s ] (X0) = 0; [ false ] () = 1; [ Marked_mark ] (X0) = 2*X0; [ from ] (X0) = 0; [ and ] (X0,X1) = 3*X1 + 2*X0; [ first ] (X0,X1) = 1*X1 + 2*X0; [ add ] (X0,X1) = 3*X1 + 2*X0; [ active ] (X0) = 1*X0; [ nil ] () = 0; [ if ] (X0,X1,X2) = 2*X2 + 2*X1 + 2*X0; [ Marked_active ] (X0) = 1*X0; [ true ] () = 0; [ cons ] (X0,X1) = 0; [ 0 ] () = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ s ] (X0) = 0; [ false ] () = 0; [ Marked_mark ] (X0) = 2*X0; [ from ] (X0) = 1; [ and ] (X0,X1) = 2*X1 + 1*X0; [ first ] (X0,X1) = 2*X1 + 2*X0; [ add ] (X0,X1) = 1*X1 + 2*X0; [ active ] (X0) = 1*X0; [ nil ] () = 0; [ if ] (X0,X1,X2) = 1*X2 + 1*X1 + 1*X0; [ Marked_active ] (X0) = 2*X0; [ true ] () = 0; [ cons ] (X0,X1) = 0; [ 0 ] () = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ s ] (X0) = 0; [ false ] () = 0; [ Marked_mark ] (X0) = 2*X0; [ from ] (X0) = 0; [ and ] (X0,X1) = 2*X1 + 2*X0; [ first ] (X0,X1) = 1*X1 + 1*X0; [ add ] (X0,X1) = 1*X1 + 1*X0; [ active ] (X0) = 1*X0; [ nil ] () = 0; [ if ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ Marked_active ] (X0) = 2*X0; [ true ] () = 0; [ cons ] (X0,X1) = 0; [ 0 ] () = 1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ s ] (X0) = 0; [ false ] () = 0; [ Marked_mark ] (X0) = 2; [ from ] (X0) = 0; [ and ] (X0,X1) = 1; [ first ] (X0,X1) = 1; [ add ] (X0,X1) = 1; [ active ] (X0) = 0; [ nil ] () = 0; [ if ] (X0,X1,X2) = 1; [ Marked_active ] (X0) = 2*X0; [ true ] () = 0; [ cons ] (X0,X1) = 0; [ 0 ] () = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ s ] (X0) = 1; [ false ] () = 0; [ Marked_mark ] (X0) = 2*X0; [ from ] (X0) = 0; [ and ] (X0,X1) = 2*X1 + 1*X0; [ first ] (X0,X1) = 2*X1 + 1*X0; [ add ] (X0,X1) = 2*X1 + 1*X0; [ active ] (X0) = 1*X0; [ nil ] () = 0; [ if ] (X0,X1,X2) = 1*X2 + 1*X1 + 2*X0; [ Marked_active ] (X0) = 2*X0; [ true ] () = 0; [ cons ] (X0,X1) = 0; [ 0 ] () = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ s ] (X0) = 1*X0 + 2; [ false ] () = 0; [ Marked_mark ] (X0) = 2*X0 + 2; [ from ] (X0) = 0; [ and ] (X0,X1) = 1*X1 + 2*X0; [ first ] (X0,X1) = 2*X1 + 2*X0; [ add ] (X0,X1) = 1*X1 + 3*X0 + 1; [ active ] (X0) = 1*X0; [ nil ] () = 0; [ if ] (X0,X1,X2) = 1*X2 + 2*X1 + 2*X0; [ Marked_active ] (X0) = 2*X0 + 2; [ true ] () = 0; [ cons ] (X0,X1) = 0; [ 0 ] () = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 2*X0; [ s ] (X0) = 0; [ false ] () = 0; [ Marked_mark ] (X0) = 2*X0 + 2; [ from ] (X0) = 1*X0 + 2; [ and ] (X0,X1) = 3*X1 + 1*X0 + 1; [ first ] (X0,X1) = 1*X1 + 1*X0; [ add ] (X0,X1) = 2*X1 + 1; [ active ] (X0) = 1*X0; [ nil ] () = 0; [ if ] (X0,X1,X2) = 2*X2 + 2*X1 + 3*X0 + 3; [ Marked_active ] (X0) = 1*X0 + 2; [ true ] () = 1; [ cons ] (X0,X1) = 0; [ 0 ] () = 0; removing < Marked_mark(and(X1,X2)),Marked_mark(X1)>< Marked_mark(if(X1,X2,X3)),Marked_mark(X1)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 1.980512 seconds (real time) Cime Exit Status: 0