- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__app(nil,YS) -> mark(YS) [2] a__app(cons(X,XS),YS) -> cons(mark(X),app(XS,YS)) [3] a__from(X) -> cons(mark(X),from(s(X))) [4] a__zWadr(nil,YS) -> nil [5] a__zWadr(XS,nil) -> nil [6] a__zWadr(cons(X,XS),cons(Y,YS)) -> cons(a__app(mark(Y),cons(mark(X),nil)),zWadr(XS,YS)) [7] a__prefix(L) -> cons(nil,zWadr(L,prefix(L))) [8] mark(app(X1,X2)) -> a__app(mark(X1),mark(X2)) [9] mark(from(X)) -> a__from(mark(X)) [10] mark(zWadr(X1,X2)) -> a__zWadr(mark(X1),mark(X2)) [11] mark(prefix(X)) -> a__prefix(mark(X)) [12] mark(nil) -> nil [13] mark(cons(X1,X2)) -> cons(mark(X1),X2) [14] mark(s(X)) -> s(mark(X)) [15] a__app(X1,X2) -> app(X1,X2) [16] a__from(X) -> from(X) [17] a__zWadr(X1,X2) -> zWadr(X1,X2) [18] a__prefix(X) -> prefix(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: { mark(nil) >= nil ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(app(X1,X2)) >= a__app(mark(X1),mark(X2)) ; mark(from(X)) >= a__from(mark(X)) ; mark(s(X)) >= s(mark(X)) ; mark(zWadr(X1,X2)) >= a__zWadr(mark(X1),mark(X2)) ; mark(prefix(X)) >= a__prefix(mark(X)) ; a__app(nil,YS) >= mark(YS) ; a__app(cons(X,XS),YS) >= cons(mark(X),app(XS,YS)) ; a__app(X1,X2) >= app(X1,X2) ; a__from(X) >= cons(mark(X),from(s(X))) ; a__from(X) >= from(X) ; a__zWadr(nil,YS) >= nil ; a__zWadr(cons(X,XS),cons(Y,YS)) >= cons(a__app(mark(Y),cons(mark(X),nil)), zWadr(XS,YS)) ; a__zWadr(XS,nil) >= nil ; a__zWadr(X1,X2) >= zWadr(X1,X2) ; a__prefix(X) >= prefix(X) ; a__prefix(L) >= cons(nil,zWadr(L,prefix(L))) ; Marked_a__zWadr(cons(X,XS),cons(Y,YS)) >= Marked_a__app(mark(Y), cons(mark(X),nil)) ; Marked_a__zWadr(cons(X,XS),cons(Y,YS)) >= Marked_mark(X) ; Marked_a__zWadr(cons(X,XS),cons(Y,YS)) >= Marked_mark(Y) ; Marked_a__from(X) >= Marked_mark(X) ; Marked_a__app(nil,YS) >= Marked_mark(YS) ; Marked_a__app(cons(X,XS),YS) >= Marked_mark(X) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(app(X1,X2)) >= Marked_a__app(mark(X1),mark(X2)) ; Marked_mark(app(X1,X2)) >= Marked_mark(X1) ; Marked_mark(app(X1,X2)) >= Marked_mark(X2) ; Marked_mark(from(X)) >= Marked_a__from(mark(X)) ; Marked_mark(from(X)) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(zWadr(X1,X2)) >= Marked_a__zWadr(mark(X1),mark(X2)) ; Marked_mark(zWadr(X1,X2)) >= Marked_mark(X1) ; Marked_mark(zWadr(X1,X2)) >= Marked_mark(X2) ; Marked_mark(prefix(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__zWadr(cons(X,XS),cons(Y,YS)) > Marked_a__app(mark(Y), cons(mark(X),nil)) ; } { Marked_a__zWadr(cons(X,XS),cons(Y,YS)) > Marked_mark(X) ; } { Marked_a__zWadr(cons(X,XS),cons(Y,YS)) > Marked_mark(Y) ; } { Marked_a__from(X) > Marked_mark(X) ; } { Marked_a__app(nil,YS) > Marked_mark(YS) ; } { Marked_a__app(cons(X,XS),YS) > Marked_mark(X) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(app(X1,X2)) > Marked_a__app(mark(X1),mark(X2)) ; } { Marked_mark(app(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(app(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(from(X)) > Marked_a__from(mark(X)) ; } { Marked_mark(from(X)) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(zWadr(X1,X2)) > Marked_a__zWadr(mark(X1),mark(X2)) ; } { Marked_mark(zWadr(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(zWadr(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(prefix(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: mark(nil) >= nil constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(app(X1,X2)) >= a__app(mark(X1),mark(X2)) constraint: mark(from(X)) >= a__from(mark(X)) constraint: mark(s(X)) >= s(mark(X)) constraint: mark(zWadr(X1,X2)) >= a__zWadr(mark(X1),mark(X2)) constraint: mark(prefix(X)) >= a__prefix(mark(X)) constraint: a__app(nil,YS) >= mark(YS) constraint: a__app(cons(X,XS),YS) >= cons(mark(X),app(XS,YS)) constraint: a__app(X1,X2) >= app(X1,X2) constraint: a__from(X) >= cons(mark(X),from(s(X))) constraint: a__from(X) >= from(X) constraint: a__zWadr(nil,YS) >= nil constraint: a__zWadr(cons(X,XS),cons(Y,YS)) >= cons(a__app(mark(Y), cons(mark(X),nil)), zWadr(XS,YS)) constraint: a__zWadr(XS,nil) >= nil constraint: a__zWadr(X1,X2) >= zWadr(X1,X2) constraint: a__prefix(X) >= prefix(X) constraint: a__prefix(L) >= cons(nil,zWadr(L,prefix(L))) constraint: Marked_a__zWadr(cons(X,XS),cons(Y,YS)) >= Marked_a__app(mark(Y), cons(mark(X),nil)) constraint: Marked_a__zWadr(cons(X,XS),cons(Y,YS)) >= Marked_mark(X) constraint: Marked_a__zWadr(cons(X,XS),cons(Y,YS)) >= Marked_mark(Y) constraint: Marked_a__from(X) >= Marked_mark(X) constraint: Marked_a__app(nil,YS) >= Marked_mark(YS) constraint: Marked_a__app(cons(X,XS),YS) >= Marked_mark(X) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(app(X1,X2)) >= Marked_a__app(mark(X1),mark(X2)) constraint: Marked_mark(app(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(app(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(s(X)) >= Marked_mark(X) constraint: Marked_mark(zWadr(X1,X2)) >= Marked_a__zWadr(mark(X1),mark(X2)) constraint: Marked_mark(zWadr(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(zWadr(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(prefix(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__app(nil,YS) -> mark(YS) [2] a__app(cons(X,XS),YS) -> cons(mark(X),app(XS,YS)) [3] a__from(X) -> cons(mark(X),from(s(X))) [4] a__zWadr(nil,YS) -> nil [5] a__zWadr(XS,nil) -> nil [6] a__zWadr(cons(X,XS),cons(Y,YS)) -> cons(a__app(mark(Y),cons(mark(X),nil)),zWadr(XS,YS)) [7] a__prefix(L) -> cons(nil,zWadr(L,prefix(L))) [8] mark(app(X1,X2)) -> a__app(mark(X1),mark(X2)) [9] mark(from(X)) -> a__from(mark(X)) [10] mark(zWadr(X1,X2)) -> a__zWadr(mark(X1),mark(X2)) [11] mark(prefix(X)) -> a__prefix(mark(X)) [12] mark(nil) -> nil [13] mark(cons(X1,X2)) -> cons(mark(X1),X2) [14] mark(s(X)) -> s(mark(X)) [15] a__app(X1,X2) -> app(X1,X2) [16] a__from(X) -> from(X) [17] a__zWadr(X1,X2) -> zWadr(X1,X2) [18] a__prefix(X) -> prefix(X) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ Marked_mark ] (X0) = 1*X0 + 1; [ a__zWadr ] (X0,X1) = 3*X1 + 2*X0 + 3; [ app ] (X0,X1) = 1*X1 + 2*X0 + 3; [ nil ] () = 0; [ prefix ] (X0) = 3*X0 + 3; [ s ] (X0) = 1*X0; [ Marked_a__from ] (X0) = 1*X0 + 3; [ a__app ] (X0,X1) = 1*X1 + 2*X0 + 3; [ zWadr ] (X0,X1) = 3*X1 + 2*X0 + 3; [ from ] (X0) = 2*X0 + 3; [ Marked_a__zWadr ] (X0,X1) = 2*X1 + 2*X0 + 2; [ cons ] (X0,X1) = 2*X0 + 2; [ a__prefix ] (X0) = 3*X0 + 3; [ a__from ] (X0) = 2*X0 + 3; [ Marked_a__app ] (X0,X1) = 1*X1 + 2*X0 + 2; removing < Marked_a__zWadr(cons(X,XS),cons(Y,YS)),Marked_mark(Y)>< Marked_mark(app(X1,X2)),Marked_mark(X1)>< Marked_mark(from(X)),Marked_a__from(mark(X))>< Marked_mark(zWadr(X1,X2)),Marked_a__zWadr(mark(X1),mark(X2))> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} Cime worked for 0.172679 seconds (real time) Cime Exit Status: 0