- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(terms(N)) -> mark(cons(recip(sqr(N)),terms(s(N)))) [2] active(sqr(0)) -> mark(0) [3] active(sqr(s(X))) -> mark(s(add(sqr(X),dbl(X)))) [4] active(dbl(0)) -> mark(0) [5] active(dbl(s(X))) -> mark(s(s(dbl(X)))) [6] active(add(0,X)) -> mark(X) [7] active(add(s(X),Y)) -> mark(s(add(X,Y))) [8] active(first(0,X)) -> mark(nil) [9] active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) [10] mark(terms(X)) -> active(terms(mark(X))) [11] mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) [12] mark(recip(X)) -> active(recip(mark(X))) [13] mark(sqr(X)) -> active(sqr(mark(X))) [14] mark(s(X)) -> active(s(mark(X))) [15] mark(0) -> active(0) [16] mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) [17] mark(dbl(X)) -> active(dbl(mark(X))) [18] mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) [19] mark(nil) -> active(nil) [20] terms(mark(X)) -> terms(X) [21] terms(active(X)) -> terms(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] recip(mark(X)) -> recip(X) [27] recip(active(X)) -> recip(X) [28] sqr(mark(X)) -> sqr(X) [29] sqr(active(X)) -> sqr(X) [30] s(mark(X)) -> s(X) [31] s(active(X)) -> s(X) [32] add(mark(X1),X2) -> add(X1,X2) [33] add(X1,mark(X2)) -> add(X1,X2) [34] add(active(X1),X2) -> add(X1,X2) [35] add(X1,active(X2)) -> add(X1,X2) [36] dbl(mark(X)) -> dbl(X) [37] dbl(active(X)) -> dbl(X) [38] first(mark(X1),X2) -> first(X1,X2) [39] first(X1,mark(X2)) -> first(X1,X2) [40] first(active(X1),X2) -> first(X1,X2) [41] first(X1,active(X2)) -> first(X1,X2) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 9 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ; mark(recip(X)) >= active(recip(mark(X))) ; mark(sqr(X)) >= active(sqr(mark(X))) ; mark(terms(X)) >= active(terms(mark(X))) ; mark(s(X)) >= active(s(mark(X))) ; mark(0) >= active(0) ; mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) ; mark(dbl(X)) >= active(dbl(mark(X))) ; mark(nil) >= active(nil) ; mark(first(X1,X2)) >= active(first(mark(X1),mark(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) ; recip(mark(X)) >= recip(X) ; recip(active(X)) >= recip(X) ; sqr(mark(X)) >= sqr(X) ; sqr(active(X)) >= sqr(X) ; terms(mark(X)) >= terms(X) ; terms(active(X)) >= terms(X) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; active(sqr(s(X))) >= mark(s(add(sqr(X),dbl(X)))) ; active(sqr(0)) >= mark(0) ; active(terms(N)) >= mark(cons(recip(sqr(N)),terms(s(N)))) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(add(0,X)) >= mark(X) ; active(dbl(s(X))) >= mark(s(s(dbl(X)))) ; active(dbl(0)) >= mark(0) ; active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) ; active(first(0,X)) >= mark(nil) ; 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) ; dbl(mark(X)) >= dbl(X) ; dbl(active(X)) >= dbl(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) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2)) ; Marked_mark(recip(X)) >= Marked_mark(X) ; Marked_mark(recip(X)) >= Marked_active(recip(mark(X))) ; Marked_mark(sqr(X)) >= Marked_mark(X) ; Marked_mark(sqr(X)) >= Marked_active(sqr(mark(X))) ; Marked_mark(terms(X)) >= Marked_mark(X) ; Marked_mark(terms(X)) >= Marked_active(terms(mark(X))) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_active(s(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(dbl(X)) >= Marked_mark(X) ; Marked_mark(dbl(X)) >= Marked_active(dbl(mark(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_active(sqr(s(X))) >= Marked_mark(s(add(sqr(X),dbl(X)))) ; Marked_active(terms(N)) >= Marked_mark(cons(recip(sqr(N)),terms(s(N)))) ; Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) ; Marked_active(add(0,X)) >= Marked_mark(X) ; Marked_active(dbl(s(X))) >= Marked_mark(s(s(dbl(X)))) ; Marked_active(first(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,first(X,Z))) ; } + Disjunctions:{ { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(cons(X1,X2)) > Marked_active(cons(mark(X1),X2)) ; } { Marked_mark(recip(X)) > Marked_mark(X) ; } { Marked_mark(recip(X)) > Marked_active(recip(mark(X))) ; } { Marked_mark(sqr(X)) > Marked_mark(X) ; } { Marked_mark(sqr(X)) > Marked_active(sqr(mark(X))) ; } { Marked_mark(terms(X)) > Marked_mark(X) ; } { Marked_mark(terms(X)) > Marked_active(terms(mark(X))) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_active(s(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(dbl(X)) > Marked_mark(X) ; } { Marked_mark(dbl(X)) > Marked_active(dbl(mark(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_active(sqr(s(X))) > Marked_mark(s(add(sqr(X),dbl(X)))) ; } { Marked_active(terms(N)) > Marked_mark(cons(recip(sqr(N)),terms(s(N)))) ; } { Marked_active(add(s(X),Y)) > Marked_mark(s(add(X,Y))) ; } { Marked_active(add(0,X)) > Marked_mark(X) ; } { Marked_active(dbl(s(X))) > Marked_mark(s(s(dbl(X)))) ; } { 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(cons(X1,X2)) >= active(cons(mark(X1),X2)) constraint: mark(recip(X)) >= active(recip(mark(X))) constraint: mark(sqr(X)) >= active(sqr(mark(X))) constraint: mark(terms(X)) >= active(terms(mark(X))) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(0) >= active(0) constraint: mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) constraint: mark(dbl(X)) >= active(dbl(mark(X))) constraint: mark(nil) >= active(nil) constraint: mark(first(X1,X2)) >= active(first(mark(X1),mark(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: recip(mark(X)) >= recip(X) constraint: recip(active(X)) >= recip(X) constraint: sqr(mark(X)) >= sqr(X) constraint: sqr(active(X)) >= sqr(X) constraint: terms(mark(X)) >= terms(X) constraint: terms(active(X)) >= terms(X) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: active(sqr(s(X))) >= mark(s(add(sqr(X),dbl(X)))) constraint: active(sqr(0)) >= mark(0) constraint: active(terms(N)) >= mark(cons(recip(sqr(N)),terms(s(N)))) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(add(0,X)) >= mark(X) constraint: active(dbl(s(X))) >= mark(s(s(dbl(X)))) constraint: active(dbl(0)) >= mark(0) constraint: active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) constraint: active(first(0,X)) >= mark(nil) 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: dbl(mark(X)) >= dbl(X) constraint: dbl(active(X)) >= dbl(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: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2)) constraint: Marked_mark(recip(X)) >= Marked_mark(X) constraint: Marked_mark(recip(X)) >= Marked_active(recip(mark(X))) constraint: Marked_mark(sqr(X)) >= Marked_mark(X) constraint: Marked_mark(sqr(X)) >= Marked_active(sqr(mark(X))) constraint: Marked_mark(terms(X)) >= Marked_mark(X) constraint: Marked_mark(terms(X)) >= Marked_active(terms(mark(X))) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(s(X)) >= Marked_active(s(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(dbl(X)) >= Marked_mark(X) constraint: Marked_mark(dbl(X)) >= Marked_active(dbl(mark(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_active(sqr(s(X))) >= Marked_mark(s(add(sqr(X),dbl(X)))) constraint: Marked_active(terms(N)) >= Marked_mark(cons(recip(sqr(N)), terms(s(N)))) constraint: Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) constraint: Marked_active(add(0,X)) >= Marked_mark(X) constraint: Marked_active(dbl(s(X))) >= Marked_mark(s(s(dbl(X)))) constraint: Marked_active(first(s(X),cons(Y,Z))) >= Marked_mark(cons( Y,first(X,Z))) APPLY CRITERIA (Subterm criterion) ST: Marked_terms -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_cons -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_recip -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_sqr -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_s -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_add -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_dbl -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_first -> 2 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ; mark(recip(X)) >= active(recip(mark(X))) ; mark(sqr(X)) >= active(sqr(mark(X))) ; mark(terms(X)) >= active(terms(mark(X))) ; mark(s(X)) >= active(s(mark(X))) ; mark(0) >= active(0) ; mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) ; mark(dbl(X)) >= active(dbl(mark(X))) ; mark(nil) >= active(nil) ; mark(first(X1,X2)) >= active(first(mark(X1),mark(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) ; recip(mark(X)) >= recip(X) ; recip(active(X)) >= recip(X) ; sqr(mark(X)) >= sqr(X) ; sqr(active(X)) >= sqr(X) ; terms(mark(X)) >= terms(X) ; terms(active(X)) >= terms(X) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; active(sqr(s(X))) >= mark(s(add(sqr(X),dbl(X)))) ; active(sqr(0)) >= mark(0) ; active(terms(N)) >= mark(cons(recip(sqr(N)),terms(s(N)))) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(add(0,X)) >= mark(X) ; active(dbl(s(X))) >= mark(s(s(dbl(X)))) ; active(dbl(0)) >= mark(0) ; active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) ; active(first(0,X)) >= mark(nil) ; 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) ; dbl(mark(X)) >= dbl(X) ; dbl(active(X)) >= dbl(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) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(recip(X)) >= Marked_mark(X) ; Marked_mark(sqr(X)) >= Marked_mark(X) ; Marked_mark(sqr(X)) >= Marked_active(sqr(mark(X))) ; Marked_mark(terms(X)) >= Marked_mark(X) ; Marked_mark(terms(X)) >= Marked_active(terms(mark(X))) ; Marked_mark(s(X)) >= Marked_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(dbl(X)) >= Marked_mark(X) ; Marked_mark(dbl(X)) >= Marked_active(dbl(mark(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_active(sqr(s(X))) >= Marked_mark(s(add(sqr(X),dbl(X)))) ; Marked_active(terms(N)) >= Marked_mark(cons(recip(sqr(N)),terms(s(N)))) ; Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) ; Marked_active(add(0,X)) >= Marked_mark(X) ; Marked_active(dbl(s(X))) >= Marked_mark(s(s(dbl(X)))) ; Marked_active(first(s(X),cons(Y,Z))) >= Marked_mark(cons(Y,first(X,Z))) ; } + Disjunctions:{ { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(recip(X)) > Marked_mark(X) ; } { Marked_mark(sqr(X)) > Marked_mark(X) ; } { Marked_mark(sqr(X)) > Marked_active(sqr(mark(X))) ; } { Marked_mark(terms(X)) > Marked_mark(X) ; } { Marked_mark(terms(X)) > Marked_active(terms(mark(X))) ; } { Marked_mark(s(X)) > Marked_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(dbl(X)) > Marked_mark(X) ; } { Marked_mark(dbl(X)) > Marked_active(dbl(mark(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_active(sqr(s(X))) > Marked_mark(s(add(sqr(X),dbl(X)))) ; } { Marked_active(terms(N)) > Marked_mark(cons(recip(sqr(N)),terms(s(N)))) ; } { Marked_active(add(s(X),Y)) > Marked_mark(s(add(X,Y))) ; } { Marked_active(add(0,X)) > Marked_mark(X) ; } { Marked_active(dbl(s(X))) > Marked_mark(s(s(dbl(X)))) ; } { 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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === STOPING TIMER virtual === constraint: mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) constraint: mark(recip(X)) >= active(recip(mark(X))) constraint: mark(sqr(X)) >= active(sqr(mark(X))) constraint: mark(terms(X)) >= active(terms(mark(X))) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(0) >= active(0) constraint: mark(add(X1,X2)) >= active(add(mark(X1),mark(X2))) constraint: mark(dbl(X)) >= active(dbl(mark(X))) constraint: mark(nil) >= active(nil) constraint: mark(first(X1,X2)) >= active(first(mark(X1),mark(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: recip(mark(X)) >= recip(X) constraint: recip(active(X)) >= recip(X) constraint: sqr(mark(X)) >= sqr(X) constraint: sqr(active(X)) >= sqr(X) constraint: terms(mark(X)) >= terms(X) constraint: terms(active(X)) >= terms(X) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: active(sqr(s(X))) >= mark(s(add(sqr(X),dbl(X)))) constraint: active(sqr(0)) >= mark(0) constraint: active(terms(N)) >= mark(cons(recip(sqr(N)),terms(s(N)))) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(add(0,X)) >= mark(X) constraint: active(dbl(s(X))) >= mark(s(s(dbl(X)))) constraint: active(dbl(0)) >= mark(0) constraint: active(first(s(X),cons(Y,Z))) >= mark(cons(Y,first(X,Z))) constraint: active(first(0,X)) >= mark(nil) 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: dbl(mark(X)) >= dbl(X) constraint: dbl(active(X)) >= dbl(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: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(recip(X)) >= Marked_mark(X) constraint: Marked_mark(sqr(X)) >= Marked_mark(X) constraint: Marked_mark(sqr(X)) >= Marked_active(sqr(mark(X))) constraint: Marked_mark(terms(X)) >= Marked_mark(X) constraint: Marked_mark(terms(X)) >= Marked_active(terms(mark(X))) constraint: Marked_mark(s(X)) >= Marked_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(dbl(X)) >= Marked_mark(X) constraint: Marked_mark(dbl(X)) >= Marked_active(dbl(mark(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_active(sqr(s(X))) >= Marked_mark(s(add(sqr(X),dbl(X)))) constraint: Marked_active(terms(N)) >= Marked_mark(cons(recip(sqr(N)), terms(s(N)))) constraint: Marked_active(add(s(X),Y)) >= Marked_mark(s(add(X,Y))) constraint: Marked_active(add(0,X)) >= Marked_mark(X) constraint: Marked_active(dbl(s(X))) >= Marked_mark(s(s(dbl(X)))) 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) ST: Marked_mark -> 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 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: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_first -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] active(terms(N)) -> mark(cons(recip(sqr(N)),terms(s(N)))) [2] active(sqr(0)) -> mark(0) [3] active(sqr(s(X))) -> mark(s(add(sqr(X),dbl(X)))) [4] active(dbl(0)) -> mark(0) [5] active(dbl(s(X))) -> mark(s(s(dbl(X)))) [6] active(add(0,X)) -> mark(X) [7] active(add(s(X),Y)) -> mark(s(add(X,Y))) [8] active(first(0,X)) -> mark(nil) [9] active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) [10] mark(terms(X)) -> active(terms(mark(X))) [11] mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) [12] mark(recip(X)) -> active(recip(mark(X))) [13] mark(sqr(X)) -> active(sqr(mark(X))) [14] mark(s(X)) -> active(s(mark(X))) [15] mark(0) -> active(0) [16] mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) [17] mark(dbl(X)) -> active(dbl(mark(X))) [18] mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) [19] mark(nil) -> active(nil) [20] terms(mark(X)) -> terms(X) [21] terms(active(X)) -> terms(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] recip(mark(X)) -> recip(X) [27] recip(active(X)) -> recip(X) [28] sqr(mark(X)) -> sqr(X) [29] sqr(active(X)) -> sqr(X) [30] s(mark(X)) -> s(X) [31] s(active(X)) -> s(X) [32] add(mark(X1),X2) -> add(X1,X2) [33] add(X1,mark(X2)) -> add(X1,X2) [34] add(active(X1),X2) -> add(X1,X2) [35] add(X1,active(X2)) -> add(X1,X2) [36] dbl(mark(X)) -> dbl(X) [37] dbl(active(X)) -> dbl(X) [38] first(mark(X1),X2) -> first(X1,X2) [39] first(X1,mark(X2)) -> first(X1,X2) [40] first(active(X1),X2) -> first(X1,X2) [41] first(X1,active(X2)) -> first(X1,X2) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 0; [ add ] (X0,X1) = 2; [ terms ] (X0) = 2; [ Marked_mark ] (X0) = 2; [ recip ] (X0) = 0; [ nil ] () = 0; [ active ] (X0) = 0; [ cons ] (X0,X1) = 0; [ dbl ] (X0) = 2; [ s ] (X0) = 0; [ Marked_active ] (X0) = 1*X0; [ sqr ] (X0) = 2; [ first ] (X0,X1) = 2; [ 0 ] () = 0; removing < Marked_mark(recip(X)),Marked_active(recip(mark(X)))> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using RPO with AFS = AFS: mark -> 0active -> 0cons -> 0 and precedence: prec (All symbols are Lex.): { recip < terms ; recip < Marked_mark ; recip < Marked_active ; sqr < terms ; sqr > s ; sqr > add ; sqr > dbl ; sqr < Marked_mark ; sqr < Marked_active ; terms > recip ; terms > sqr ; terms > s ; terms > add ; terms > dbl ; s < sqr ; s < terms ; s < add ; s < dbl ; s < Marked_mark ; s < Marked_active ; add < sqr ; add < terms ; add > s ; add < Marked_mark ; add < Marked_active ; dbl < sqr ; dbl < terms ; dbl > s ; dbl < Marked_mark ; dbl < Marked_active ; nil < first ; first > nil ; Marked_mark > recip ; Marked_mark > sqr ; Marked_mark > s ; Marked_mark > add ; Marked_mark > dbl ; Marked_mark = Marked_active ; Marked_active > recip ; Marked_active > sqr ; Marked_active > s ; Marked_active > add ; Marked_active > dbl ; Marked_active = Marked_mark ; } removing < Marked_active(sqr(s(X))),Marked_mark(s(add(sqr(X),dbl(X))))>< Marked_mark(terms(X)),Marked_mark(X)>< Marked_mark(sqr(X)),Marked_mark(X)>< Marked_mark(add(X1,X2)),Marked_mark(X1)>< Marked_mark(dbl(X)),Marked_mark(X)>< Marked_mark(first(X1,X2)),Marked_mark(X2)> [ { 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 1.060392 seconds (real time) Cime Exit Status: 0