- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(fst(0,Z)) -> mark(nil) [2] active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z))) [3] active(from(X)) -> mark(cons(X,from(s(X)))) [4] active(add(0,X)) -> mark(X) [5] active(add(s(X),Y)) -> mark(s(add(X,Y))) [6] active(len(nil)) -> mark(0) [7] active(len(cons(X,Z))) -> mark(s(len(Z))) [8] mark(fst(X1,X2)) -> active(fst(mark(X1),mark(X2))) [9] mark(0) -> active(0) [10] mark(nil) -> active(nil) [11] mark(s(X)) -> active(s(X)) [12] mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) [13] mark(from(X)) -> active(from(mark(X))) [14] mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) [15] mark(len(X)) -> active(len(mark(X))) [16] fst(mark(X1),X2) -> fst(X1,X2) [17] fst(X1,mark(X2)) -> fst(X1,X2) [18] fst(active(X1),X2) -> fst(X1,X2) [19] fst(X1,active(X2)) -> fst(X1,X2) [20] s(mark(X)) -> s(X) [21] s(active(X)) -> s(X) [22] cons(mark(X1),X2) -> cons(X1,X2) [23] cons(X1,mark(X2)) -> cons(X1,X2) [24] cons(active(X1),X2) -> cons(X1,X2) [25] cons(X1,active(X2)) -> cons(X1,X2) [26] from(mark(X)) -> from(X) [27] from(active(X)) -> from(X) [28] add(mark(X1),X2) -> add(X1,X2) [29] add(X1,mark(X2)) -> add(X1,X2) [30] add(active(X1),X2) -> add(X1,X2) [31] add(X1,active(X2)) -> add(X1,X2) [32] len(mark(X)) -> len(X) [33] len(active(X)) -> len(X) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 7 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(nil) >= active(nil) ; mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) ; mark(0) >= active(0) ; mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ; mark(s(X)) >= active(s(X)) ; mark(from(X)) >= active(from(mark(X))) ; mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) ; mark(len(X)) >= active(len(mark(X))) ; active(fst(0,Z)) >= mark(nil) ; active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(len(nil)) >= mark(0) ; active(len(cons(X,Z))) >= mark(s(len(Z))) ; fst(mark(X1),X2) >= fst(X1,X2) ; fst(active(X1),X2) >= fst(X1,X2) ; fst(X1,mark(X2)) >= fst(X1,X2) ; fst(X1,active(X2)) >= fst(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) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; 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) ; len(mark(X)) >= len(X) ; len(active(X)) >= len(X) ; Marked_mark(fst(X1,X2)) >= Marked_mark(X1) ; Marked_mark(fst(X1,X2)) >= Marked_mark(X2) ; Marked_mark(fst(X1,X2)) >= Marked_active(fst(mark(X1),mark(X2))) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2)) ; Marked_mark(s(X)) >= Marked_active(s(X)) ; Marked_mark(from(X)) >= Marked_mark(X) ; Marked_mark(from(X)) >= Marked_active(from(mark(X))) ; Marked_mark(add(X1,X2)) >= Marked_mark(X1) ; Marked_mark(add(X1,X2)) >= Marked_mark(X2) ; Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),mark(X2))) ; Marked_mark(len(X)) >= Marked_mark(X) ; Marked_mark(len(X)) >= Marked_active(len(mark(X))) ; Marked_active(fst(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,fst(X,Z))) ; Marked_active(from(X)) >= Marked_mark(cons(X,from(s(X)))) ; Marked_active(add(0,X)) >= Marked_mark(X) ; Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) ; Marked_active(len(cons(X,Z))) >= Marked_mark(s(len(Z))) ; } + Disjunctions:{ { Marked_mark(fst(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(fst(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(fst(X1,X2)) > Marked_active(fst(mark(X1),mark(X2))) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(cons(X1,X2)) > Marked_active(cons(mark(X1),X2)) ; } { Marked_mark(s(X)) > Marked_active(s(X)) ; } { Marked_mark(from(X)) > Marked_mark(X) ; } { Marked_mark(from(X)) > Marked_active(from(mark(X))) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(add(X1,X2)) > Marked_active(add(mark(X1),mark(X2))) ; } { Marked_mark(len(X)) > Marked_mark(X) ; } { Marked_mark(len(X)) > Marked_active(len(mark(X))) ; } { Marked_active(fst(s(X),cons(Y,Z))) > Marked_mark(cons(Y,fst(X,Z))) ; } { Marked_active(from(X)) > Marked_mark(cons(X,from(s(X)))) ; } { Marked_active(add(0,X)) > Marked_mark(X) ; } { Marked_active(add(s(X),Y)) > Marked_mark(s(add(X,Y))) ; } { Marked_active(len(cons(X,Z))) > Marked_mark(s(len(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(nil) >= active(nil) constraint: mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) constraint: mark(0) >= active(0) constraint: mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) constraint: mark(s(X)) >= active(s(X)) constraint: mark(from(X)) >= active(from(mark(X))) constraint: mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) constraint: mark(len(X)) >= active(len(mark(X))) constraint: active(fst(0,Z)) >= mark(nil) constraint: active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(len(nil)) >= mark(0) constraint: active(len(cons(X,Z))) >= mark(s(len(Z))) constraint: fst(mark(X1),X2) >= fst(X1,X2) constraint: fst(active(X1),X2) >= fst(X1,X2) constraint: fst(X1,mark(X2)) >= fst(X1,X2) constraint: fst(X1,active(X2)) >= fst(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: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) 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: len(mark(X)) >= len(X) constraint: len(active(X)) >= len(X) constraint: Marked_mark(fst(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(fst(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(fst(X1,X2)) >= Marked_active(fst(mark(X1),mark(X2))) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2)) constraint: Marked_mark(s(X)) >= Marked_active(s(X)) constraint: Marked_mark(from(X)) >= Marked_mark(X) constraint: Marked_mark(from(X)) >= Marked_active(from(mark(X))) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),mark(X2))) constraint: Marked_mark(len(X)) >= Marked_mark(X) constraint: Marked_mark(len(X)) >= Marked_active(len(mark(X))) constraint: Marked_active(fst(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,fst(X,Z))) constraint: Marked_active(from(X)) >= Marked_mark(cons(X,from(s(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(len(cons(X,Z))) >= Marked_mark(s(len(Z))) APPLY CRITERIA (Subterm criterion) ST: Marked_fst -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_s -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_cons -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_from -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_add -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_len -> 1 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(nil) >= active(nil) ; mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) ; mark(0) >= active(0) ; mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ; mark(s(X)) >= active(s(X)) ; mark(from(X)) >= active(from(mark(X))) ; mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) ; mark(len(X)) >= active(len(mark(X))) ; active(fst(0,Z)) >= mark(nil) ; active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(len(nil)) >= mark(0) ; active(len(cons(X,Z))) >= mark(s(len(Z))) ; fst(mark(X1),X2) >= fst(X1,X2) ; fst(active(X1),X2) >= fst(X1,X2) ; fst(X1,mark(X2)) >= fst(X1,X2) ; fst(X1,active(X2)) >= fst(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) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; 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) ; len(mark(X)) >= len(X) ; len(active(X)) >= len(X) ; Marked_mark(fst(X1,X2)) >= Marked_mark(X1) ; Marked_mark(fst(X1,X2)) >= Marked_mark(X2) ; Marked_mark(fst(X1,X2)) >= Marked_active(fst(mark(X1),mark(X2))) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(from(X)) >= Marked_mark(X) ; Marked_mark(from(X)) >= Marked_active(from(mark(X))) ; Marked_mark(add(X1,X2)) >= Marked_mark(X1) ; Marked_mark(add(X1,X2)) >= Marked_mark(X2) ; Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),mark(X2))) ; Marked_mark(len(X)) >= Marked_mark(X) ; Marked_mark(len(X)) >= Marked_active(len(mark(X))) ; Marked_active(fst(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,fst(X,Z))) ; Marked_active(from(X)) >= Marked_mark(cons(X,from(s(X)))) ; Marked_active(add(0,X)) >= Marked_mark(X) ; Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) ; Marked_active(len(cons(X,Z))) >= Marked_mark(s(len(Z))) ; } + Disjunctions:{ { Marked_mark(fst(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(fst(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(fst(X1,X2)) > Marked_active(fst(mark(X1),mark(X2))) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(from(X)) > Marked_mark(X) ; } { Marked_mark(from(X)) > Marked_active(from(mark(X))) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(add(X1,X2)) > Marked_active(add(mark(X1),mark(X2))) ; } { Marked_mark(len(X)) > Marked_mark(X) ; } { Marked_mark(len(X)) > Marked_active(len(mark(X))) ; } { Marked_active(fst(s(X),cons(Y,Z))) > Marked_mark(cons(Y,fst(X,Z))) ; } { Marked_active(from(X)) > Marked_mark(cons(X,from(s(X)))) ; } { Marked_active(add(0,X)) > Marked_mark(X) ; } { Marked_active(add(s(X),Y)) > Marked_mark(s(add(X,Y))) ; } { Marked_active(len(cons(X,Z))) > Marked_mark(s(len(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(nil) >= active(nil) constraint: mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) constraint: mark(0) >= active(0) constraint: mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) constraint: mark(s(X)) >= active(s(X)) constraint: mark(from(X)) >= active(from(mark(X))) constraint: mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) constraint: mark(len(X)) >= active(len(mark(X))) constraint: active(fst(0,Z)) >= mark(nil) constraint: active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(len(nil)) >= mark(0) constraint: active(len(cons(X,Z))) >= mark(s(len(Z))) constraint: fst(mark(X1),X2) >= fst(X1,X2) constraint: fst(active(X1),X2) >= fst(X1,X2) constraint: fst(X1,mark(X2)) >= fst(X1,X2) constraint: fst(X1,active(X2)) >= fst(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: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) 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: len(mark(X)) >= len(X) constraint: len(active(X)) >= len(X) constraint: Marked_mark(fst(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(fst(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(fst(X1,X2)) >= Marked_active(fst(mark(X1),mark(X2))) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(from(X)) >= Marked_mark(X) constraint: Marked_mark(from(X)) >= Marked_active(from(mark(X))) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),mark(X2))) constraint: Marked_mark(len(X)) >= Marked_mark(X) constraint: Marked_mark(len(X)) >= Marked_active(len(mark(X))) constraint: Marked_active(fst(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,fst(X,Z))) constraint: Marked_active(from(X)) >= Marked_mark(cons(X,from(s(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(len(cons(X,Z))) >= Marked_mark(s(len(Z))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(nil) >= active(nil) ; mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) ; mark(0) >= active(0) ; mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ; mark(s(X)) >= active(s(X)) ; mark(from(X)) >= active(from(mark(X))) ; mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) ; mark(len(X)) >= active(len(mark(X))) ; active(fst(0,Z)) >= mark(nil) ; active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(len(nil)) >= mark(0) ; active(len(cons(X,Z))) >= mark(s(len(Z))) ; fst(mark(X1),X2) >= fst(X1,X2) ; fst(active(X1),X2) >= fst(X1,X2) ; fst(X1,mark(X2)) >= fst(X1,X2) ; fst(X1,active(X2)) >= fst(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) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; 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) ; len(mark(X)) >= len(X) ; len(active(X)) >= len(X) ; Marked_mark(fst(X1,X2)) >= Marked_mark(X1) ; Marked_mark(fst(X1,X2)) >= Marked_mark(X2) ; Marked_mark(fst(X1,X2)) >= Marked_active(fst(mark(X1),mark(X2))) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(from(X)) >= Marked_mark(X) ; Marked_mark(from(X)) >= Marked_active(from(mark(X))) ; Marked_mark(add(X1,X2)) >= Marked_mark(X1) ; Marked_mark(add(X1,X2)) >= Marked_mark(X2) ; Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),mark(X2))) ; Marked_mark(len(X)) >= Marked_mark(X) ; Marked_mark(len(X)) >= Marked_active(len(mark(X))) ; Marked_active(fst(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,fst(X,Z))) ; Marked_active(from(X)) >= Marked_mark(cons(X,from(s(X)))) ; Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) ; Marked_active(len(cons(X,Z))) >= Marked_mark(s(len(Z))) ; } + Disjunctions:{ { Marked_mark(fst(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(fst(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(fst(X1,X2)) > Marked_active(fst(mark(X1),mark(X2))) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(from(X)) > Marked_mark(X) ; } { Marked_mark(from(X)) > Marked_active(from(mark(X))) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(add(X1,X2)) > Marked_active(add(mark(X1),mark(X2))) ; } { Marked_mark(len(X)) > Marked_mark(X) ; } { Marked_mark(len(X)) > Marked_active(len(mark(X))) ; } { Marked_active(fst(s(X),cons(Y,Z))) > Marked_mark(cons(Y,fst(X,Z))) ; } { Marked_active(from(X)) > Marked_mark(cons(X,from(s(X)))) ; } { Marked_active(add(s(X),Y)) > Marked_mark(s(add(X,Y))) ; } { Marked_active(len(cons(X,Z))) > Marked_mark(s(len(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(nil) >= active(nil) constraint: mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) constraint: mark(0) >= active(0) constraint: mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) constraint: mark(s(X)) >= active(s(X)) constraint: mark(from(X)) >= active(from(mark(X))) constraint: mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) constraint: mark(len(X)) >= active(len(mark(X))) constraint: active(fst(0,Z)) >= mark(nil) constraint: active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(len(nil)) >= mark(0) constraint: active(len(cons(X,Z))) >= mark(s(len(Z))) constraint: fst(mark(X1),X2) >= fst(X1,X2) constraint: fst(active(X1),X2) >= fst(X1,X2) constraint: fst(X1,mark(X2)) >= fst(X1,X2) constraint: fst(X1,active(X2)) >= fst(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: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) 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: len(mark(X)) >= len(X) constraint: len(active(X)) >= len(X) constraint: Marked_mark(fst(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(fst(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(fst(X1,X2)) >= Marked_active(fst(mark(X1),mark(X2))) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(from(X)) >= Marked_mark(X) constraint: Marked_mark(from(X)) >= Marked_active(from(mark(X))) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(add(X1,X2)) >= Marked_active(add(mark(X1),mark(X2))) constraint: Marked_mark(len(X)) >= Marked_mark(X) constraint: Marked_mark(len(X)) >= Marked_active(len(mark(X))) constraint: Marked_active(fst(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,fst(X,Z))) constraint: Marked_active(from(X)) >= Marked_mark(cons(X,from(s(X)))) constraint: Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) constraint: Marked_active(len(cons(X,Z))) >= Marked_mark(s(len(Z))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(nil) >= active(nil) ; mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) ; mark(0) >= active(0) ; mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ; mark(s(X)) >= active(s(X)) ; mark(from(X)) >= active(from(mark(X))) ; mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) ; mark(len(X)) >= active(len(mark(X))) ; active(fst(0,Z)) >= mark(nil) ; active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(len(nil)) >= mark(0) ; active(len(cons(X,Z))) >= mark(s(len(Z))) ; fst(mark(X1),X2) >= fst(X1,X2) ; fst(active(X1),X2) >= fst(X1,X2) ; fst(X1,mark(X2)) >= fst(X1,X2) ; fst(X1,active(X2)) >= fst(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) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; 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) ; len(mark(X)) >= len(X) ; len(active(X)) >= len(X) ; Marked_mark(fst(X1,X2)) >= Marked_mark(X1) ; Marked_mark(fst(X1,X2)) >= Marked_mark(X2) ; Marked_mark(fst(X1,X2)) >= Marked_active(fst(mark(X1),mark(X2))) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(from(X)) >= Marked_mark(X) ; Marked_mark(from(X)) >= Marked_active(from(mark(X))) ; Marked_mark(len(X)) >= Marked_mark(X) ; Marked_mark(len(X)) >= Marked_active(len(mark(X))) ; Marked_active(fst(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,fst(X,Z))) ; Marked_active(from(X)) >= Marked_mark(cons(X,from(s(X)))) ; Marked_active(len(cons(X,Z))) >= Marked_mark(s(len(Z))) ; } + Disjunctions:{ { Marked_mark(fst(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(fst(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(fst(X1,X2)) > Marked_active(fst(mark(X1),mark(X2))) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(from(X)) > Marked_mark(X) ; } { Marked_mark(from(X)) > Marked_active(from(mark(X))) ; } { Marked_mark(len(X)) > Marked_mark(X) ; } { Marked_mark(len(X)) > Marked_active(len(mark(X))) ; } { Marked_active(fst(s(X),cons(Y,Z))) > Marked_mark(cons(Y,fst(X,Z))) ; } { Marked_active(from(X)) > Marked_mark(cons(X,from(s(X)))) ; } { Marked_active(len(cons(X,Z))) > Marked_mark(s(len(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(nil) >= active(nil) constraint: mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) constraint: mark(0) >= active(0) constraint: mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) constraint: mark(s(X)) >= active(s(X)) constraint: mark(from(X)) >= active(from(mark(X))) constraint: mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) constraint: mark(len(X)) >= active(len(mark(X))) constraint: active(fst(0,Z)) >= mark(nil) constraint: active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(len(nil)) >= mark(0) constraint: active(len(cons(X,Z))) >= mark(s(len(Z))) constraint: fst(mark(X1),X2) >= fst(X1,X2) constraint: fst(active(X1),X2) >= fst(X1,X2) constraint: fst(X1,mark(X2)) >= fst(X1,X2) constraint: fst(X1,active(X2)) >= fst(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: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) 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: len(mark(X)) >= len(X) constraint: len(active(X)) >= len(X) constraint: Marked_mark(fst(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(fst(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(fst(X1,X2)) >= Marked_active(fst(mark(X1),mark(X2))) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(from(X)) >= Marked_mark(X) constraint: Marked_mark(from(X)) >= Marked_active(from(mark(X))) constraint: Marked_mark(len(X)) >= Marked_mark(X) constraint: Marked_mark(len(X)) >= Marked_active(len(mark(X))) constraint: Marked_active(fst(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,fst(X,Z))) constraint: Marked_active(from(X)) >= Marked_mark(cons(X,from(s(X)))) constraint: Marked_active(len(cons(X,Z))) >= Marked_mark(s(len(Z))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(nil) >= active(nil) ; mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) ; mark(0) >= active(0) ; mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ; mark(s(X)) >= active(s(X)) ; mark(from(X)) >= active(from(mark(X))) ; mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) ; mark(len(X)) >= active(len(mark(X))) ; active(fst(0,Z)) >= mark(nil) ; active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(len(nil)) >= mark(0) ; active(len(cons(X,Z))) >= mark(s(len(Z))) ; fst(mark(X1),X2) >= fst(X1,X2) ; fst(active(X1),X2) >= fst(X1,X2) ; fst(X1,mark(X2)) >= fst(X1,X2) ; fst(X1,active(X2)) >= fst(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) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; 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) ; len(mark(X)) >= len(X) ; len(active(X)) >= len(X) ; Marked_mark(fst(X1,X2)) >= Marked_mark(X1) ; Marked_mark(fst(X1,X2)) >= Marked_mark(X2) ; Marked_mark(fst(X1,X2)) >= Marked_active(fst(mark(X1),mark(X2))) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(len(X)) >= Marked_mark(X) ; Marked_mark(len(X)) >= Marked_active(len(mark(X))) ; Marked_active(fst(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,fst(X,Z))) ; Marked_active(len(cons(X,Z))) >= Marked_mark(s(len(Z))) ; } + Disjunctions:{ { Marked_mark(fst(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(fst(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(fst(X1,X2)) > Marked_active(fst(mark(X1),mark(X2))) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(len(X)) > Marked_mark(X) ; } { Marked_mark(len(X)) > Marked_active(len(mark(X))) ; } { Marked_active(fst(s(X),cons(Y,Z))) > Marked_mark(cons(Y,fst(X,Z))) ; } { Marked_active(len(cons(X,Z))) > Marked_mark(s(len(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(nil) >= active(nil) constraint: mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) constraint: mark(0) >= active(0) constraint: mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) constraint: mark(s(X)) >= active(s(X)) constraint: mark(from(X)) >= active(from(mark(X))) constraint: mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) constraint: mark(len(X)) >= active(len(mark(X))) constraint: active(fst(0,Z)) >= mark(nil) constraint: active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(len(nil)) >= mark(0) constraint: active(len(cons(X,Z))) >= mark(s(len(Z))) constraint: fst(mark(X1),X2) >= fst(X1,X2) constraint: fst(active(X1),X2) >= fst(X1,X2) constraint: fst(X1,mark(X2)) >= fst(X1,X2) constraint: fst(X1,active(X2)) >= fst(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: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) 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: len(mark(X)) >= len(X) constraint: len(active(X)) >= len(X) constraint: Marked_mark(fst(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(fst(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(fst(X1,X2)) >= Marked_active(fst(mark(X1),mark(X2))) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(len(X)) >= Marked_mark(X) constraint: Marked_mark(len(X)) >= Marked_active(len(mark(X))) constraint: Marked_active(fst(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,fst(X,Z))) constraint: Marked_active(len(cons(X,Z))) >= Marked_mark(s(len(Z))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(nil) >= active(nil) ; mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) ; mark(0) >= active(0) ; mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ; mark(s(X)) >= active(s(X)) ; mark(from(X)) >= active(from(mark(X))) ; mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) ; mark(len(X)) >= active(len(mark(X))) ; active(fst(0,Z)) >= mark(nil) ; active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(len(nil)) >= mark(0) ; active(len(cons(X,Z))) >= mark(s(len(Z))) ; fst(mark(X1),X2) >= fst(X1,X2) ; fst(active(X1),X2) >= fst(X1,X2) ; fst(X1,mark(X2)) >= fst(X1,X2) ; fst(X1,active(X2)) >= fst(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) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; 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) ; len(mark(X)) >= len(X) ; len(active(X)) >= len(X) ; Marked_mark(fst(X1,X2)) >= Marked_active(fst(mark(X1),mark(X2))) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(len(X)) >= Marked_mark(X) ; Marked_mark(len(X)) >= Marked_active(len(mark(X))) ; Marked_active(len(cons(X,Z))) >= Marked_mark(s(len(Z))) ; } + Disjunctions:{ { Marked_mark(fst(X1,X2)) > Marked_active(fst(mark(X1),mark(X2))) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(len(X)) > Marked_mark(X) ; } { Marked_mark(len(X)) > Marked_active(len(mark(X))) ; } { Marked_active(len(cons(X,Z))) > Marked_mark(s(len(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(nil) >= active(nil) constraint: mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) constraint: mark(0) >= active(0) constraint: mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) constraint: mark(s(X)) >= active(s(X)) constraint: mark(from(X)) >= active(from(mark(X))) constraint: mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) constraint: mark(len(X)) >= active(len(mark(X))) constraint: active(fst(0,Z)) >= mark(nil) constraint: active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(len(nil)) >= mark(0) constraint: active(len(cons(X,Z))) >= mark(s(len(Z))) constraint: fst(mark(X1),X2) >= fst(X1,X2) constraint: fst(active(X1),X2) >= fst(X1,X2) constraint: fst(X1,mark(X2)) >= fst(X1,X2) constraint: fst(X1,active(X2)) >= fst(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: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) 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: len(mark(X)) >= len(X) constraint: len(active(X)) >= len(X) constraint: Marked_mark(fst(X1,X2)) >= Marked_active(fst(mark(X1),mark(X2))) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(len(X)) >= Marked_mark(X) constraint: Marked_mark(len(X)) >= Marked_active(len(mark(X))) constraint: Marked_active(len(cons(X,Z))) >= Marked_mark(s(len(Z))) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(nil) >= active(nil) ; mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) ; mark(0) >= active(0) ; mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ; mark(s(X)) >= active(s(X)) ; mark(from(X)) >= active(from(mark(X))) ; mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) ; mark(len(X)) >= active(len(mark(X))) ; active(fst(0,Z)) >= mark(nil) ; active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(len(nil)) >= mark(0) ; active(len(cons(X,Z))) >= mark(s(len(Z))) ; fst(mark(X1),X2) >= fst(X1,X2) ; fst(active(X1),X2) >= fst(X1,X2) ; fst(X1,mark(X2)) >= fst(X1,X2) ; fst(X1,active(X2)) >= fst(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) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; from(mark(X)) >= from(X) ; from(active(X)) >= from(X) ; 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) ; len(mark(X)) >= len(X) ; len(active(X)) >= len(X) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(len(X)) >= Marked_mark(X) ; Marked_mark(len(X)) >= Marked_active(len(mark(X))) ; Marked_active(len(cons(X,Z))) >= Marked_mark(s(len(Z))) ; } + Disjunctions:{ { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(len(X)) > Marked_mark(X) ; } { Marked_mark(len(X)) > Marked_active(len(mark(X))) ; } { Marked_active(len(cons(X,Z))) > Marked_mark(s(len(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(nil) >= active(nil) constraint: mark(fst(X1,X2)) >= active(fst(mark(X1),mark(X2))) constraint: mark(0) >= active(0) constraint: mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) constraint: mark(s(X)) >= active(s(X)) constraint: mark(from(X)) >= active(from(mark(X))) constraint: mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) constraint: mark(len(X)) >= active(len(mark(X))) constraint: active(fst(0,Z)) >= mark(nil) constraint: active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(len(nil)) >= mark(0) constraint: active(len(cons(X,Z))) >= mark(s(len(Z))) constraint: fst(mark(X1),X2) >= fst(X1,X2) constraint: fst(active(X1),X2) >= fst(X1,X2) constraint: fst(X1,mark(X2)) >= fst(X1,X2) constraint: fst(X1,active(X2)) >= fst(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: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: from(mark(X)) >= from(X) constraint: from(active(X)) >= from(X) 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: len(mark(X)) >= len(X) constraint: len(active(X)) >= len(X) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(len(X)) >= Marked_mark(X) constraint: Marked_mark(len(X)) >= Marked_active(len(mark(X))) constraint: Marked_active(len(cons(X,Z))) >= Marked_mark(s(len(Z))) 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_fst -> 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_cons -> 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_add -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] active(fst(0,Z)) -> mark(nil) [2] active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z))) [3] active(from(X)) -> mark(cons(X,from(s(X)))) [4] active(add(0,X)) -> mark(X) [5] active(add(s(X),Y)) -> mark(s(add(X,Y))) [6] active(len(nil)) -> mark(0) [7] active(len(cons(X,Z))) -> mark(s(len(Z))) [8] mark(fst(X1,X2)) -> active(fst(mark(X1),mark(X2))) [9] mark(0) -> active(0) [10] mark(nil) -> active(nil) [11] mark(s(X)) -> active(s(X)) [12] mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) [13] mark(from(X)) -> active(from(mark(X))) [14] mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) [15] mark(len(X)) -> active(len(mark(X))) [16] fst(mark(X1),X2) -> fst(X1,X2) [17] fst(X1,mark(X2)) -> fst(X1,X2) [18] fst(active(X1),X2) -> fst(X1,X2) [19] fst(X1,active(X2)) -> fst(X1,X2) [20] s(mark(X)) -> s(X) [21] s(active(X)) -> s(X) [22] cons(mark(X1),X2) -> cons(X1,X2) [23] cons(X1,mark(X2)) -> cons(X1,X2) [24] cons(active(X1),X2) -> cons(X1,X2) [25] cons(X1,active(X2)) -> cons(X1,X2) [26] from(mark(X)) -> from(X) [27] from(active(X)) -> from(X) [28] add(mark(X1),X2) -> add(X1,X2) [29] add(X1,mark(X2)) -> add(X1,X2) [30] add(active(X1),X2) -> add(X1,X2) [31] add(X1,active(X2)) -> add(X1,X2) [32] len(mark(X)) -> len(X) [33] len(active(X)) -> len(X) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ Marked_mark ] (X0) = 2; [ add ] (X0,X1) = 2; [ 0 ] () = 0; [ active ] (X0) = 0; [ s ] (X0) = 0; [ nil ] () = 0; [ Marked_active ] (X0) = 1*X0; [ len ] (X0) = 2; [ cons ] (X0,X1) = 0; [ fst ] (X0,X1) = 2; [ from ] (X0) = 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ Marked_mark ] (X0) = 2*X0; [ add ] (X0,X1) = 2*X1 + 2*X0; [ 0 ] () = 1; [ active ] (X0) = 1*X0; [ s ] (X0) = 0; [ nil ] () = 1; [ Marked_active ] (X0) = 2*X0; [ len ] (X0) = 2*X0; [ cons ] (X0,X1) = 2*X0; [ fst ] (X0,X1) = 2*X1 + 2*X0; [ from ] (X0) = 2*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 2*X0; [ Marked_mark ] (X0) = 2*X0; [ add ] (X0,X1) = 2*X1 + 2*X0 + 2; [ 0 ] () = 0; [ active ] (X0) = 1*X0; [ s ] (X0) = 0; [ nil ] () = 0; [ Marked_active ] (X0) = 1*X0; [ len ] (X0) = 1*X0; [ cons ] (X0,X1) = 1*X0; [ fst ] (X0,X1) = 2*X1 + 2*X0; [ from ] (X0) = 2*X0; removing < Marked_mark(add(X1,X2)),Marked_mark(X2)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 2*X0; [ Marked_mark ] (X0) = 2*X0; [ add ] (X0,X1) = 2*X1; [ 0 ] () = 0; [ active ] (X0) = 1*X0; [ s ] (X0) = 0; [ nil ] () = 0; [ Marked_active ] (X0) = 1*X0; [ len ] (X0) = 2*X0; [ cons ] (X0,X1) = 1*X0; [ fst ] (X0,X1) = 2*X1 + 2*X0; [ from ] (X0) = 2*X0 + 1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ Marked_mark ] (X0) = 2*X0; [ add ] (X0,X1) = 2*X1; [ 0 ] () = 0; [ active ] (X0) = 1*X0; [ s ] (X0) = 0; [ nil ] () = 0; [ Marked_active ] (X0) = 2*X0; [ len ] (X0) = 2*X0; [ cons ] (X0,X1) = 1*X0; [ fst ] (X0,X1) = 2*X1 + 2*X0 + 1; [ from ] (X0) = 1*X0; removing < Marked_mark(fst(X1,X2)),Marked_mark(X1)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ Marked_mark ] (X0) = 2; [ add ] (X0,X1) = 0; [ 0 ] () = 0; [ active ] (X0) = 0; [ s ] (X0) = 0; [ nil ] () = 0; [ Marked_active ] (X0) = 2*X0; [ len ] (X0) = 1; [ cons ] (X0,X1) = 0; [ fst ] (X0,X1) = 0; [ from ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 2*X0; [ Marked_mark ] (X0) = 2*X0; [ add ] (X0,X1) = 2*X1; [ 0 ] () = 0; [ active ] (X0) = 1*X0; [ s ] (X0) = 0; [ nil ] () = 0; [ Marked_active ] (X0) = 0; [ len ] (X0) = 2*X0 + 1; [ cons ] (X0,X1) = 1*X0; [ fst ] (X0,X1) = 2*X1; [ from ] (X0) = 2*X0; removing [ { 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 1.508010 seconds (real time) Cime Exit Status: 0