- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] fst(0,Z) -> nil [2] fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z))) [3] from(X) -> cons(X,n__from(n__s(X))) [4] add(0,X) -> X [5] add(s(X),Y) -> s(n__add(activate(X),Y)) [6] len(nil) -> 0 [7] len(cons(X,Z)) -> s(n__len(activate(Z))) [8] fst(X1,X2) -> n__fst(X1,X2) [9] from(X) -> n__from(X) [10] s(X) -> n__s(X) [11] add(X1,X2) -> n__add(X1,X2) [12] len(X) -> n__len(X) [13] activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2)) [14] activate(n__from(X)) -> from(activate(X)) [15] activate(n__s(X)) -> s(X) [16] activate(n__add(X1,X2)) -> add(activate(X1),activate(X2)) [17] activate(n__len(X)) -> len(activate(X)) [18] activate(X) -> 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: { fst(0,Z) >= nil ; fst(s(X),cons(Y,Z)) >= cons(Y,n__fst(activate(X),activate(Z))) ; fst(X1,X2) >= n__fst(X1,X2) ; activate(n__fst(X1,X2)) >= fst(activate(X1),activate(X2)) ; activate(n__from(X)) >= from(activate(X)) ; activate(n__s(X)) >= s(X) ; activate(n__add(X1,X2)) >= add(activate(X1),activate(X2)) ; activate(n__len(X)) >= len(activate(X)) ; activate(X) >= X ; s(X) >= n__s(X) ; from(X) >= cons(X,n__from(n__s(X))) ; from(X) >= n__from(X) ; add(0,X) >= X ; add(s(X),Y) >= s(n__add(activate(X),Y)) ; add(X1,X2) >= n__add(X1,X2) ; len(nil) >= 0 ; len(cons(X,Z)) >= s(n__len(activate(Z))) ; len(X) >= n__len(X) ; Marked_activate(n__fst(X1,X2)) >= Marked_activate(X1) ; Marked_activate(n__fst(X1,X2)) >= Marked_activate(X2) ; Marked_activate(n__fst(X1,X2)) >= Marked_fst(activate(X1),activate(X2)) ; Marked_activate(n__from(X)) >= Marked_activate(X) ; Marked_activate(n__add(X1,X2)) >= Marked_activate(X1) ; Marked_activate(n__add(X1,X2)) >= Marked_activate(X2) ; Marked_activate(n__add(X1,X2)) >= Marked_add(activate(X1),activate(X2)) ; Marked_activate(n__len(X)) >= Marked_activate(X) ; Marked_activate(n__len(X)) >= Marked_len(activate(X)) ; Marked_len(cons(X,Z)) >= Marked_activate(Z) ; Marked_add(s(X),Y) >= Marked_activate(X) ; Marked_fst(s(X),cons(Y,Z)) >= Marked_activate(X) ; Marked_fst(s(X),cons(Y,Z)) >= Marked_activate(Z) ; } + Disjunctions:{ { Marked_activate(n__fst(X1,X2)) > Marked_activate(X1) ; } { Marked_activate(n__fst(X1,X2)) > Marked_activate(X2) ; } { Marked_activate(n__fst(X1,X2)) > Marked_fst(activate(X1),activate(X2)) ; } { Marked_activate(n__from(X)) > Marked_activate(X) ; } { Marked_activate(n__add(X1,X2)) > Marked_activate(X1) ; } { Marked_activate(n__add(X1,X2)) > Marked_activate(X2) ; } { Marked_activate(n__add(X1,X2)) > Marked_add(activate(X1),activate(X2)) ; } { Marked_activate(n__len(X)) > Marked_activate(X) ; } { Marked_activate(n__len(X)) > Marked_len(activate(X)) ; } { Marked_len(cons(X,Z)) > Marked_activate(Z) ; } { Marked_add(s(X),Y) > Marked_activate(X) ; } { Marked_fst(s(X),cons(Y,Z)) > Marked_activate(X) ; } { Marked_fst(s(X),cons(Y,Z)) > Marked_activate(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: fst(0,Z) >= nil constraint: fst(s(X),cons(Y,Z)) >= cons(Y,n__fst(activate(X),activate(Z))) constraint: fst(X1,X2) >= n__fst(X1,X2) constraint: activate(n__fst(X1,X2)) >= fst(activate(X1),activate(X2)) constraint: activate(n__from(X)) >= from(activate(X)) constraint: activate(n__s(X)) >= s(X) constraint: activate(n__add(X1,X2)) >= add(activate(X1),activate(X2)) constraint: activate(n__len(X)) >= len(activate(X)) constraint: activate(X) >= X constraint: s(X) >= n__s(X) constraint: from(X) >= cons(X,n__from(n__s(X))) constraint: from(X) >= n__from(X) constraint: add(0,X) >= X constraint: add(s(X),Y) >= s(n__add(activate(X),Y)) constraint: add(X1,X2) >= n__add(X1,X2) constraint: len(nil) >= 0 constraint: len(cons(X,Z)) >= s(n__len(activate(Z))) constraint: len(X) >= n__len(X) constraint: Marked_activate(n__fst(X1,X2)) >= Marked_activate(X1) constraint: Marked_activate(n__fst(X1,X2)) >= Marked_activate(X2) constraint: Marked_activate(n__fst(X1,X2)) >= Marked_fst(activate(X1), activate(X2)) constraint: Marked_activate(n__from(X)) >= Marked_activate(X) constraint: Marked_activate(n__add(X1,X2)) >= Marked_activate(X1) constraint: Marked_activate(n__add(X1,X2)) >= Marked_activate(X2) constraint: Marked_activate(n__add(X1,X2)) >= Marked_add(activate(X1), activate(X2)) constraint: Marked_activate(n__len(X)) >= Marked_activate(X) constraint: Marked_activate(n__len(X)) >= Marked_len(activate(X)) constraint: Marked_len(cons(X,Z)) >= Marked_activate(Z) constraint: Marked_add(s(X),Y) >= Marked_activate(X) constraint: Marked_fst(s(X),cons(Y,Z)) >= Marked_activate(X) constraint: Marked_fst(s(X),cons(Y,Z)) >= Marked_activate(Z) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { fst(0,Z) >= nil ; fst(s(X),cons(Y,Z)) >= cons(Y,n__fst(activate(X),activate(Z))) ; fst(X1,X2) >= n__fst(X1,X2) ; activate(n__fst(X1,X2)) >= fst(activate(X1),activate(X2)) ; activate(n__from(X)) >= from(activate(X)) ; activate(n__s(X)) >= s(X) ; activate(n__add(X1,X2)) >= add(activate(X1),activate(X2)) ; activate(n__len(X)) >= len(activate(X)) ; activate(X) >= X ; s(X) >= n__s(X) ; from(X) >= cons(X,n__from(n__s(X))) ; from(X) >= n__from(X) ; add(0,X) >= X ; add(s(X),Y) >= s(n__add(activate(X),Y)) ; add(X1,X2) >= n__add(X1,X2) ; len(nil) >= 0 ; len(cons(X,Z)) >= s(n__len(activate(Z))) ; len(X) >= n__len(X) ; Marked_activate(n__fst(X1,X2)) >= Marked_activate(X1) ; Marked_activate(n__fst(X1,X2)) >= Marked_activate(X2) ; Marked_activate(n__fst(X1,X2)) >= Marked_fst(activate(X1),activate(X2)) ; Marked_activate(n__from(X)) >= Marked_activate(X) ; Marked_fst(s(X),cons(Y,Z)) >= Marked_activate(X) ; Marked_fst(s(X),cons(Y,Z)) >= Marked_activate(Z) ; } + Disjunctions:{ { Marked_activate(n__fst(X1,X2)) > Marked_activate(X1) ; } { Marked_activate(n__fst(X1,X2)) > Marked_activate(X2) ; } { Marked_activate(n__fst(X1,X2)) > Marked_fst(activate(X1),activate(X2)) ; } { Marked_activate(n__from(X)) > Marked_activate(X) ; } { Marked_fst(s(X),cons(Y,Z)) > Marked_activate(X) ; } { Marked_fst(s(X),cons(Y,Z)) > Marked_activate(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: fst(0,Z) >= nil constraint: fst(s(X),cons(Y,Z)) >= cons(Y,n__fst(activate(X),activate(Z))) constraint: fst(X1,X2) >= n__fst(X1,X2) constraint: activate(n__fst(X1,X2)) >= fst(activate(X1),activate(X2)) constraint: activate(n__from(X)) >= from(activate(X)) constraint: activate(n__s(X)) >= s(X) constraint: activate(n__add(X1,X2)) >= add(activate(X1),activate(X2)) constraint: activate(n__len(X)) >= len(activate(X)) constraint: activate(X) >= X constraint: s(X) >= n__s(X) constraint: from(X) >= cons(X,n__from(n__s(X))) constraint: from(X) >= n__from(X) constraint: add(0,X) >= X constraint: add(s(X),Y) >= s(n__add(activate(X),Y)) constraint: add(X1,X2) >= n__add(X1,X2) constraint: len(nil) >= 0 constraint: len(cons(X,Z)) >= s(n__len(activate(Z))) constraint: len(X) >= n__len(X) constraint: Marked_activate(n__fst(X1,X2)) >= Marked_activate(X1) constraint: Marked_activate(n__fst(X1,X2)) >= Marked_activate(X2) constraint: Marked_activate(n__fst(X1,X2)) >= Marked_fst(activate(X1), activate(X2)) constraint: Marked_activate(n__from(X)) >= Marked_activate(X) constraint: Marked_fst(s(X),cons(Y,Z)) >= Marked_activate(X) constraint: Marked_fst(s(X),cons(Y,Z)) >= Marked_activate(Z) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_activate -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] fst(0,Z) -> nil [2] fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z))) [3] from(X) -> cons(X,n__from(n__s(X))) [4] add(0,X) -> X [5] add(s(X),Y) -> s(n__add(activate(X),Y)) [6] len(nil) -> 0 [7] len(cons(X,Z)) -> s(n__len(activate(Z))) [8] fst(X1,X2) -> n__fst(X1,X2) [9] from(X) -> n__from(X) [10] s(X) -> n__s(X) [11] add(X1,X2) -> n__add(X1,X2) [12] len(X) -> n__len(X) [13] activate(n__fst(X1,X2)) -> fst(activate(X1),activate(X2)) [14] activate(n__from(X)) -> from(activate(X)) [15] activate(n__s(X)) -> s(X) [16] activate(n__add(X1,X2)) -> add(activate(X1),activate(X2)) [17] activate(n__len(X)) -> len(activate(X)) [18] activate(X) -> X , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ nil ] () = 0; [ Marked_add ] (X0,X1) = 2*X0 + 2; [ n__s ] (X0) = 1*X0; [ n__fst ] (X0,X1) = 2*X1 + 2*X0; [ len ] (X0) = 2*X0 + 3; [ 0 ] () = 0; [ add ] (X0,X1) = 2*X1 + 2*X0 + 1; [ s ] (X0) = 1*X0; [ Marked_activate ] (X0) = 1*X0 + 1; [ fst ] (X0,X1) = 2*X1 + 2*X0; [ from ] (X0) = 2*X0; [ activate ] (X0) = 1*X0; [ n__len ] (X0) = 2*X0 + 3; [ cons ] (X0,X1) = 1*X1; [ Marked_fst ] (X0,X1) = 1*X1 + 1*X0 + 1; [ n__add ] (X0,X1) = 2*X1 + 2*X0 + 1; [ n__from ] (X0) = 2*X0; [ Marked_len ] (X0) = 2*X0 + 2; removing < Marked_activate(n__add(X1,X2)),Marked_activate(X2)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ nil ] () = 0; [ n__s ] (X0) = 1*X0; [ n__fst ] (X0,X1) = 1*X1 + 1*X0 + 2; [ len ] (X0) = 0; [ 0 ] () = 0; [ add ] (X0,X1) = 1*X1; [ s ] (X0) = 1*X0; [ Marked_activate ] (X0) = 2*X0; [ fst ] (X0,X1) = 1*X1 + 1*X0 + 2; [ from ] (X0) = 2*X0; [ activate ] (X0) = 1*X0; [ n__len ] (X0) = 0; [ cons ] (X0,X1) = 1*X1; [ Marked_fst ] (X0,X1) = 2*X1 + 2*X0 + 2; [ n__add ] (X0,X1) = 1*X1; [ n__from ] (X0) = 2*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} ]} ]} Cime worked for 0.196942 seconds (real time) Cime Exit Status: 0