- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__fst(0,Z) -> nil [2] a__fst(s(X),cons(Y,Z)) -> cons(mark(Y),fst(X,Z)) [3] a__from(X) -> cons(mark(X),from(s(X))) [4] a__add(0,X) -> mark(X) [5] a__add(s(X),Y) -> s(add(X,Y)) [6] a__len(nil) -> 0 [7] a__len(cons(X,Z)) -> s(len(Z)) [8] mark(fst(X1,X2)) -> a__fst(mark(X1),mark(X2)) [9] mark(from(X)) -> a__from(mark(X)) [10] mark(add(X1,X2)) -> a__add(mark(X1),mark(X2)) [11] mark(len(X)) -> a__len(mark(X)) [12] mark(0) -> 0 [13] mark(s(X)) -> s(X) [14] mark(nil) -> nil [15] mark(cons(X1,X2)) -> cons(mark(X1),X2) [16] a__fst(X1,X2) -> fst(X1,X2) [17] a__from(X) -> from(X) [18] a__add(X1,X2) -> add(X1,X2) [19] a__len(X) -> len(X) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__fst(0,Z) >= nil ; a__fst(s(X),cons(Y,Z)) >= cons(mark(Y),fst(X,Z)) ; a__fst(X1,X2) >= fst(X1,X2) ; mark(nil) >= nil ; mark(0) >= 0 ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(fst(X1,X2)) >= a__fst(mark(X1),mark(X2)) ; mark(s(X)) >= s(X) ; mark(from(X)) >= a__from(mark(X)) ; mark(add(X1,X2)) >= a__add(mark(X1),mark(X2)) ; mark(len(X)) >= a__len(mark(X)) ; a__from(X) >= cons(mark(X),from(s(X))) ; a__from(X) >= from(X) ; a__add(0,X) >= mark(X) ; a__add(s(X),Y) >= s(add(X,Y)) ; a__add(X1,X2) >= add(X1,X2) ; a__len(nil) >= 0 ; a__len(cons(X,Z)) >= s(len(Z)) ; a__len(X) >= len(X) ; Marked_a__add(0,X) >= Marked_mark(X) ; Marked_a__from(X) >= Marked_mark(X) ; Marked_a__fst(s(X),cons(Y,Z)) >= Marked_mark(Y) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(fst(X1,X2)) >= Marked_a__fst(mark(X1),mark(X2)) ; Marked_mark(fst(X1,X2)) >= Marked_mark(X1) ; Marked_mark(fst(X1,X2)) >= Marked_mark(X2) ; Marked_mark(from(X)) >= Marked_a__from(mark(X)) ; Marked_mark(from(X)) >= Marked_mark(X) ; Marked_mark(add(X1,X2)) >= Marked_a__add(mark(X1),mark(X2)) ; Marked_mark(add(X1,X2)) >= Marked_mark(X1) ; Marked_mark(add(X1,X2)) >= Marked_mark(X2) ; Marked_mark(len(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__add(0,X) > Marked_mark(X) ; } { Marked_a__from(X) > Marked_mark(X) ; } { Marked_a__fst(s(X),cons(Y,Z)) > Marked_mark(Y) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(fst(X1,X2)) > Marked_a__fst(mark(X1),mark(X2)) ; } { Marked_mark(fst(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(fst(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(from(X)) > Marked_a__from(mark(X)) ; } { Marked_mark(from(X)) > Marked_mark(X) ; } { Marked_mark(add(X1,X2)) > Marked_a__add(mark(X1),mark(X2)) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(add(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(len(X)) > 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: a__fst(0,Z) >= nil constraint: a__fst(s(X),cons(Y,Z)) >= cons(mark(Y),fst(X,Z)) constraint: a__fst(X1,X2) >= fst(X1,X2) constraint: mark(nil) >= nil constraint: mark(0) >= 0 constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(fst(X1,X2)) >= a__fst(mark(X1),mark(X2)) constraint: mark(s(X)) >= s(X) constraint: mark(from(X)) >= a__from(mark(X)) constraint: mark(add(X1,X2)) >= a__add(mark(X1),mark(X2)) constraint: mark(len(X)) >= a__len(mark(X)) constraint: a__from(X) >= cons(mark(X),from(s(X))) constraint: a__from(X) >= from(X) constraint: a__add(0,X) >= mark(X) constraint: a__add(s(X),Y) >= s(add(X,Y)) constraint: a__add(X1,X2) >= add(X1,X2) constraint: a__len(nil) >= 0 constraint: a__len(cons(X,Z)) >= s(len(Z)) constraint: a__len(X) >= len(X) constraint: Marked_a__add(0,X) >= Marked_mark(X) constraint: Marked_a__from(X) >= Marked_mark(X) constraint: Marked_a__fst(s(X),cons(Y,Z)) >= Marked_mark(Y) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(fst(X1,X2)) >= Marked_a__fst(mark(X1),mark(X2)) constraint: Marked_mark(fst(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(fst(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(from(X)) >= Marked_a__from(mark(X)) constraint: Marked_mark(from(X)) >= Marked_mark(X) constraint: Marked_mark(add(X1,X2)) >= Marked_a__add(mark(X1),mark(X2)) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(add(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(len(X)) >= 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: SOLVED { TRS termination of: [1] a__fst(0,Z) -> nil [2] a__fst(s(X),cons(Y,Z)) -> cons(mark(Y),fst(X,Z)) [3] a__from(X) -> cons(mark(X),from(s(X))) [4] a__add(0,X) -> mark(X) [5] a__add(s(X),Y) -> s(add(X,Y)) [6] a__len(nil) -> 0 [7] a__len(cons(X,Z)) -> s(len(Z)) [8] mark(fst(X1,X2)) -> a__fst(mark(X1),mark(X2)) [9] mark(from(X)) -> a__from(mark(X)) [10] mark(add(X1,X2)) -> a__add(mark(X1),mark(X2)) [11] mark(len(X)) -> a__len(mark(X)) [12] mark(0) -> 0 [13] mark(s(X)) -> s(X) [14] mark(nil) -> nil [15] mark(cons(X1,X2)) -> cons(mark(X1),X2) [16] a__fst(X1,X2) -> fst(X1,X2) [17] a__from(X) -> from(X) [18] a__add(X1,X2) -> add(X1,X2) [19] a__len(X) -> len(X) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ nil ] () = 0; [ Marked_a__fst ] (X0,X1) = 1*X1 + 1*X0 + 3; [ a__from ] (X0) = 2*X0 + 2; [ mark ] (X0) = 1*X0; [ len ] (X0) = 2*X0 + 1; [ 0 ] () = 1; [ add ] (X0,X1) = 1*X1 + 2*X0 + 2; [ s ] (X0) = 1; [ Marked_a__add ] (X0,X1) = 1*X1 + 1*X0 + 3; [ a__fst ] (X0,X1) = 1*X1 + 1*X0 + 2; [ Marked_mark ] (X0) = 1*X0 + 2; [ a__add ] (X0,X1) = 1*X1 + 2*X0 + 2; [ fst ] (X0,X1) = 1*X1 + 1*X0 + 2; [ cons ] (X0,X1) = 2*X0; [ a__len ] (X0) = 2*X0 + 1; [ from ] (X0) = 2*X0 + 2; [ Marked_a__from ] (X0) = 1*X0 + 2; removing < Marked_mark(fst(X1,X2)),Marked_mark(X1)>< Marked_mark(from(X)),Marked_a__from(mark(X))>< Marked_mark(add(X1,X2)),Marked_a__add(mark(X1),mark(X2))> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} Cime worked for 0.102449 seconds (real time) Cime Exit Status: 0