- : 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] active(cons(X1,X2)) -> cons(active(X1),X2) [9] active(fst(X1,X2)) -> fst(active(X1),X2) [10] active(fst(X1,X2)) -> fst(X1,active(X2)) [11] active(from(X)) -> from(active(X)) [12] active(add(X1,X2)) -> add(active(X1),X2) [13] active(add(X1,X2)) -> add(X1,active(X2)) [14] active(len(X)) -> len(active(X)) [15] cons(mark(X1),X2) -> mark(cons(X1,X2)) [16] fst(mark(X1),X2) -> mark(fst(X1,X2)) [17] fst(X1,mark(X2)) -> mark(fst(X1,X2)) [18] from(mark(X)) -> mark(from(X)) [19] add(mark(X1),X2) -> mark(add(X1,X2)) [20] add(X1,mark(X2)) -> mark(add(X1,X2)) [21] len(mark(X)) -> mark(len(X)) [22] proper(0) -> ok(0) [23] proper(s(X)) -> s(proper(X)) [24] proper(nil) -> ok(nil) [25] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) [26] proper(fst(X1,X2)) -> fst(proper(X1),proper(X2)) [27] proper(from(X)) -> from(proper(X)) [28] proper(add(X1,X2)) -> add(proper(X1),proper(X2)) [29] proper(len(X)) -> len(proper(X)) [30] s(ok(X)) -> ok(s(X)) [31] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) [32] fst(ok(X1),ok(X2)) -> ok(fst(X1,X2)) [33] from(ok(X)) -> ok(from(X)) [34] add(ok(X1),ok(X2)) -> ok(add(X1,X2)) [35] len(ok(X)) -> ok(len(X)) [36] top(mark(X)) -> top(proper(X)) [37] top(ok(X)) -> top(active(X)) 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: { active(fst(0,Z)) >= mark(nil) ; active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) ; active(fst(X1,X2)) >= fst(active(X1),X2) ; active(fst(X1,X2)) >= fst(X1,active(X2)) ; active(cons(X1,X2)) >= cons(active(X1),X2) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; active(from(X)) >= from(active(X)) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(add(X1,X2)) >= add(active(X1),X2) ; active(add(X1,X2)) >= add(X1,active(X2)) ; active(len(nil)) >= mark(0) ; active(len(cons(X,Z))) >= mark(s(len(Z))) ; active(len(X)) >= len(active(X)) ; fst(mark(X1),X2) >= mark(fst(X1,X2)) ; fst(ok(X1),ok(X2)) >= ok(fst(X1,X2)) ; fst(X1,mark(X2)) >= mark(fst(X1,X2)) ; cons(mark(X1),X2) >= mark(cons(X1,X2)) ; cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ; s(ok(X)) >= ok(s(X)) ; from(mark(X)) >= mark(from(X)) ; from(ok(X)) >= ok(from(X)) ; add(mark(X1),X2) >= mark(add(X1,X2)) ; add(ok(X1),ok(X2)) >= ok(add(X1,X2)) ; add(X1,mark(X2)) >= mark(add(X1,X2)) ; len(mark(X)) >= mark(len(X)) ; len(ok(X)) >= ok(len(X)) ; proper(nil) >= ok(nil) ; proper(fst(X1,X2)) >= fst(proper(X1),proper(X2)) ; proper(0) >= ok(0) ; proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ; proper(s(X)) >= s(proper(X)) ; proper(from(X)) >= from(proper(X)) ; proper(add(X1,X2)) >= add(proper(X1),proper(X2)) ; proper(len(X)) >= len(proper(X)) ; top(mark(X)) >= top(proper(X)) ; top(ok(X)) >= top(active(X)) ; Marked_top(mark(X)) >= Marked_top(proper(X)) ; Marked_top(ok(X)) >= Marked_top(active(X)) ; } + Disjunctions:{ { Marked_top(mark(X)) > Marked_top(proper(X)) ; } { Marked_top(ok(X)) > Marked_top(active(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: active(fst(0,Z)) >= mark(nil) constraint: active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) constraint: active(fst(X1,X2)) >= fst(active(X1),X2) constraint: active(fst(X1,X2)) >= fst(X1,active(X2)) constraint: active(cons(X1,X2)) >= cons(active(X1),X2) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: active(from(X)) >= from(active(X)) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(add(X1,X2)) >= add(active(X1),X2) constraint: active(add(X1,X2)) >= add(X1,active(X2)) constraint: active(len(nil)) >= mark(0) constraint: active(len(cons(X,Z))) >= mark(s(len(Z))) constraint: active(len(X)) >= len(active(X)) constraint: fst(mark(X1),X2) >= mark(fst(X1,X2)) constraint: fst(ok(X1),ok(X2)) >= ok(fst(X1,X2)) constraint: fst(X1,mark(X2)) >= mark(fst(X1,X2)) constraint: cons(mark(X1),X2) >= mark(cons(X1,X2)) constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) constraint: s(ok(X)) >= ok(s(X)) constraint: from(mark(X)) >= mark(from(X)) constraint: from(ok(X)) >= ok(from(X)) constraint: add(mark(X1),X2) >= mark(add(X1,X2)) constraint: add(ok(X1),ok(X2)) >= ok(add(X1,X2)) constraint: add(X1,mark(X2)) >= mark(add(X1,X2)) constraint: len(mark(X)) >= mark(len(X)) constraint: len(ok(X)) >= ok(len(X)) constraint: proper(nil) >= ok(nil) constraint: proper(fst(X1,X2)) >= fst(proper(X1),proper(X2)) constraint: proper(0) >= ok(0) constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) constraint: proper(s(X)) >= s(proper(X)) constraint: proper(from(X)) >= from(proper(X)) constraint: proper(add(X1,X2)) >= add(proper(X1),proper(X2)) constraint: proper(len(X)) >= len(proper(X)) constraint: top(mark(X)) >= top(proper(X)) constraint: top(ok(X)) >= top(active(X)) constraint: Marked_top(mark(X)) >= Marked_top(proper(X)) constraint: Marked_top(ok(X)) >= Marked_top(active(X)) APPLY CRITERIA (Subterm criterion) ST: Marked_proper -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_active -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_s -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_cons -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_fst -> 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: { active(fst(0,Z)) >= mark(nil) ; active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) ; active(fst(X1,X2)) >= fst(active(X1),X2) ; active(fst(X1,X2)) >= fst(X1,active(X2)) ; active(cons(X1,X2)) >= cons(active(X1),X2) ; active(from(X)) >= mark(cons(X,from(s(X)))) ; active(from(X)) >= from(active(X)) ; active(add(0,X)) >= mark(X) ; active(add(s(X),Y)) >= mark(s(add(X,Y))) ; active(add(X1,X2)) >= add(active(X1),X2) ; active(add(X1,X2)) >= add(X1,active(X2)) ; active(len(nil)) >= mark(0) ; active(len(cons(X,Z))) >= mark(s(len(Z))) ; active(len(X)) >= len(active(X)) ; fst(mark(X1),X2) >= mark(fst(X1,X2)) ; fst(ok(X1),ok(X2)) >= ok(fst(X1,X2)) ; fst(X1,mark(X2)) >= mark(fst(X1,X2)) ; cons(mark(X1),X2) >= mark(cons(X1,X2)) ; cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ; s(ok(X)) >= ok(s(X)) ; from(mark(X)) >= mark(from(X)) ; from(ok(X)) >= ok(from(X)) ; add(mark(X1),X2) >= mark(add(X1,X2)) ; add(ok(X1),ok(X2)) >= ok(add(X1,X2)) ; add(X1,mark(X2)) >= mark(add(X1,X2)) ; len(mark(X)) >= mark(len(X)) ; len(ok(X)) >= ok(len(X)) ; proper(nil) >= ok(nil) ; proper(fst(X1,X2)) >= fst(proper(X1),proper(X2)) ; proper(0) >= ok(0) ; proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ; proper(s(X)) >= s(proper(X)) ; proper(from(X)) >= from(proper(X)) ; proper(add(X1,X2)) >= add(proper(X1),proper(X2)) ; proper(len(X)) >= len(proper(X)) ; top(mark(X)) >= top(proper(X)) ; top(ok(X)) >= top(active(X)) ; Marked_top(ok(X)) >= Marked_top(active(X)) ; } + Disjunctions:{ { Marked_top(ok(X)) > Marked_top(active(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: active(fst(0,Z)) >= mark(nil) constraint: active(fst(s(X),cons(Y,Z))) >= mark(cons(Y,fst(X,Z))) constraint: active(fst(X1,X2)) >= fst(active(X1),X2) constraint: active(fst(X1,X2)) >= fst(X1,active(X2)) constraint: active(cons(X1,X2)) >= cons(active(X1),X2) constraint: active(from(X)) >= mark(cons(X,from(s(X)))) constraint: active(from(X)) >= from(active(X)) constraint: active(add(0,X)) >= mark(X) constraint: active(add(s(X),Y)) >= mark(s(add(X,Y))) constraint: active(add(X1,X2)) >= add(active(X1),X2) constraint: active(add(X1,X2)) >= add(X1,active(X2)) constraint: active(len(nil)) >= mark(0) constraint: active(len(cons(X,Z))) >= mark(s(len(Z))) constraint: active(len(X)) >= len(active(X)) constraint: fst(mark(X1),X2) >= mark(fst(X1,X2)) constraint: fst(ok(X1),ok(X2)) >= ok(fst(X1,X2)) constraint: fst(X1,mark(X2)) >= mark(fst(X1,X2)) constraint: cons(mark(X1),X2) >= mark(cons(X1,X2)) constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) constraint: s(ok(X)) >= ok(s(X)) constraint: from(mark(X)) >= mark(from(X)) constraint: from(ok(X)) >= ok(from(X)) constraint: add(mark(X1),X2) >= mark(add(X1,X2)) constraint: add(ok(X1),ok(X2)) >= ok(add(X1,X2)) constraint: add(X1,mark(X2)) >= mark(add(X1,X2)) constraint: len(mark(X)) >= mark(len(X)) constraint: len(ok(X)) >= ok(len(X)) constraint: proper(nil) >= ok(nil) constraint: proper(fst(X1,X2)) >= fst(proper(X1),proper(X2)) constraint: proper(0) >= ok(0) constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) constraint: proper(s(X)) >= s(proper(X)) constraint: proper(from(X)) >= from(proper(X)) constraint: proper(add(X1,X2)) >= add(proper(X1),proper(X2)) constraint: proper(len(X)) >= len(proper(X)) constraint: top(mark(X)) >= top(proper(X)) constraint: top(ok(X)) >= top(active(X)) constraint: Marked_top(ok(X)) >= Marked_top(active(X)) 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_cons -> 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_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] active(cons(X1,X2)) -> cons(active(X1),X2) [9] active(fst(X1,X2)) -> fst(active(X1),X2) [10] active(fst(X1,X2)) -> fst(X1,active(X2)) [11] active(from(X)) -> from(active(X)) [12] active(add(X1,X2)) -> add(active(X1),X2) [13] active(add(X1,X2)) -> add(X1,active(X2)) [14] active(len(X)) -> len(active(X)) [15] cons(mark(X1),X2) -> mark(cons(X1,X2)) [16] fst(mark(X1),X2) -> mark(fst(X1,X2)) [17] fst(X1,mark(X2)) -> mark(fst(X1,X2)) [18] from(mark(X)) -> mark(from(X)) [19] add(mark(X1),X2) -> mark(add(X1,X2)) [20] add(X1,mark(X2)) -> mark(add(X1,X2)) [21] len(mark(X)) -> mark(len(X)) [22] proper(0) -> ok(0) [23] proper(s(X)) -> s(proper(X)) [24] proper(nil) -> ok(nil) [25] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) [26] proper(fst(X1,X2)) -> fst(proper(X1),proper(X2)) [27] proper(from(X)) -> from(proper(X)) [28] proper(add(X1,X2)) -> add(proper(X1),proper(X2)) [29] proper(len(X)) -> len(proper(X)) [30] s(ok(X)) -> ok(s(X)) [31] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) [32] fst(ok(X1),ok(X2)) -> ok(fst(X1,X2)) [33] from(ok(X)) -> ok(from(X)) [34] add(ok(X1),ok(X2)) -> ok(add(X1,X2)) [35] len(ok(X)) -> ok(len(X)) [36] top(mark(X)) -> top(proper(X)) [37] top(ok(X)) -> top(active(X)) , CRITERION: MDP [ { DP termination of: