- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(U11(tt,M,N)) -> mark(U12(tt,M,N)) [2] active(U12(tt,M,N)) -> mark(s(plus(N,M))) [3] active(plus(N,0)) -> mark(N) [4] active(plus(N,s(M))) -> mark(U11(tt,M,N)) [5] mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) [6] mark(tt) -> active(tt) [7] mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) [8] mark(s(X)) -> active(s(mark(X))) [9] mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) [10] mark(0) -> active(0) [11] U11(mark(X1),X2,X3) -> U11(X1,X2,X3) [12] U11(X1,mark(X2),X3) -> U11(X1,X2,X3) [13] U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) [14] U11(active(X1),X2,X3) -> U11(X1,X2,X3) [15] U11(X1,active(X2),X3) -> U11(X1,X2,X3) [16] U11(X1,X2,active(X3)) -> U11(X1,X2,X3) [17] U12(mark(X1),X2,X3) -> U12(X1,X2,X3) [18] U12(X1,mark(X2),X3) -> U12(X1,X2,X3) [19] U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) [20] U12(active(X1),X2,X3) -> U12(X1,X2,X3) [21] U12(X1,active(X2),X3) -> U12(X1,X2,X3) [22] U12(X1,X2,active(X3)) -> U12(X1,X2,X3) [23] s(mark(X)) -> s(X) [24] s(active(X)) -> s(X) [25] plus(mark(X1),X2) -> plus(X1,X2) [26] plus(X1,mark(X2)) -> plus(X1,X2) [27] plus(active(X1),X2) -> plus(X1,X2) [28] plus(X1,active(X2)) -> plus(X1,X2) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 5 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(U12(X1,X2,X3)) >= active(U12(mark(X1),X2,X3)) ; mark(tt) >= active(tt) ; mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) ; mark(s(X)) >= active(s(mark(X))) ; mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ; mark(0) >= active(0) ; U12(mark(X1),X2,X3) >= U12(X1,X2,X3) ; U12(active(X1),X2,X3) >= U12(X1,X2,X3) ; U12(X1,mark(X2),X3) >= U12(X1,X2,X3) ; U12(X1,active(X2),X3) >= U12(X1,X2,X3) ; U12(X1,X2,mark(X3)) >= U12(X1,X2,X3) ; U12(X1,X2,active(X3)) >= U12(X1,X2,X3) ; active(U12(tt,M,N)) >= mark(s(plus(N,M))) ; active(U11(tt,M,N)) >= mark(U12(tt,M,N)) ; active(plus(N,s(M))) >= mark(U11(tt,M,N)) ; active(plus(N,0)) >= mark(N) ; U11(mark(X1),X2,X3) >= U11(X1,X2,X3) ; U11(active(X1),X2,X3) >= U11(X1,X2,X3) ; U11(X1,mark(X2),X3) >= U11(X1,X2,X3) ; U11(X1,active(X2),X3) >= U11(X1,X2,X3) ; U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) ; U11(X1,X2,active(X3)) >= U11(X1,X2,X3) ; s(mark(X)) >= s(X) ; s(active(X)) >= s(X) ; plus(mark(X1),X2) >= plus(X1,X2) ; plus(active(X1),X2) >= plus(X1,X2) ; plus(X1,mark(X2)) >= plus(X1,X2) ; plus(X1,active(X2)) >= plus(X1,X2) ; Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U12(X1,X2,X3)) >= Marked_active(U12(mark(X1),X2,X3)) ; Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) ; Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_active(s(mark(X))) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ; Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ; Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) ; Marked_active(U12(tt,M,N)) >= Marked_mark(s(plus(N,M))) ; Marked_active(U11(tt,M,N)) >= Marked_mark(U12(tt,M,N)) ; Marked_active(plus(N,s(M))) >= Marked_mark(U11(tt,M,N)) ; Marked_active(plus(N,0)) >= Marked_mark(N) ; } + Disjunctions:{ { Marked_mark(U12(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U12(X1,X2,X3)) > Marked_active(U12(mark(X1),X2,X3)) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_mark(X1) ; } { Marked_mark(U11(X1,X2,X3)) > Marked_active(U11(mark(X1),X2,X3)) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_active(s(mark(X))) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(plus(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(plus(X1,X2)) > Marked_active(plus(mark(X1),mark(X2))) ; } { Marked_active(U12(tt,M,N)) > Marked_mark(s(plus(N,M))) ; } { Marked_active(U11(tt,M,N)) > Marked_mark(U12(tt,M,N)) ; } { Marked_active(plus(N,s(M))) > Marked_mark(U11(tt,M,N)) ; } { Marked_active(plus(N,0)) > Marked_mark(N) ; } } === 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(U12(X1,X2,X3)) >= active(U12(mark(X1),X2,X3)) constraint: mark(tt) >= active(tt) constraint: mark(U11(X1,X2,X3)) >= active(U11(mark(X1),X2,X3)) constraint: mark(s(X)) >= active(s(mark(X))) constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) constraint: mark(0) >= active(0) constraint: U12(mark(X1),X2,X3) >= U12(X1,X2,X3) constraint: U12(active(X1),X2,X3) >= U12(X1,X2,X3) constraint: U12(X1,mark(X2),X3) >= U12(X1,X2,X3) constraint: U12(X1,active(X2),X3) >= U12(X1,X2,X3) constraint: U12(X1,X2,mark(X3)) >= U12(X1,X2,X3) constraint: U12(X1,X2,active(X3)) >= U12(X1,X2,X3) constraint: active(U12(tt,M,N)) >= mark(s(plus(N,M))) constraint: active(U11(tt,M,N)) >= mark(U12(tt,M,N)) constraint: active(plus(N,s(M))) >= mark(U11(tt,M,N)) constraint: active(plus(N,0)) >= mark(N) constraint: U11(mark(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(active(X1),X2,X3) >= U11(X1,X2,X3) constraint: U11(X1,mark(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,active(X2),X3) >= U11(X1,X2,X3) constraint: U11(X1,X2,mark(X3)) >= U11(X1,X2,X3) constraint: U11(X1,X2,active(X3)) >= U11(X1,X2,X3) constraint: s(mark(X)) >= s(X) constraint: s(active(X)) >= s(X) constraint: plus(mark(X1),X2) >= plus(X1,X2) constraint: plus(active(X1),X2) >= plus(X1,X2) constraint: plus(X1,mark(X2)) >= plus(X1,X2) constraint: plus(X1,active(X2)) >= plus(X1,X2) constraint: Marked_mark(U12(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U12(X1,X2,X3)) >= Marked_active(U12(mark(X1),X2,X3)) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_mark(X1) constraint: Marked_mark(U11(X1,X2,X3)) >= Marked_active(U11(mark(X1),X2,X3)) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(s(X)) >= Marked_active(s(mark(X))) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) constraint: Marked_active(U12(tt,M,N)) >= Marked_mark(s(plus(N,M))) constraint: Marked_active(U11(tt,M,N)) >= Marked_mark(U12(tt,M,N)) constraint: Marked_active(plus(N,s(M))) >= Marked_mark(U11(tt,M,N)) constraint: Marked_active(plus(N,0)) >= Marked_mark(N) APPLY CRITERIA (Subterm criterion) ST: Marked_U11 -> 3 APPLY CRITERIA (Subterm criterion) ST: Marked_U12 -> 3 APPLY CRITERIA (Subterm criterion) ST: Marked_s -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_plus -> 2 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 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_U11 -> 2 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_U11 -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_U12 -> 2 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_U12 -> 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_plus -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] active(U11(tt,M,N)) -> mark(U12(tt,M,N)) [2] active(U12(tt,M,N)) -> mark(s(plus(N,M))) [3] active(plus(N,0)) -> mark(N) [4] active(plus(N,s(M))) -> mark(U11(tt,M,N)) [5] mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) [6] mark(tt) -> active(tt) [7] mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) [8] mark(s(X)) -> active(s(mark(X))) [9] mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) [10] mark(0) -> active(0) [11] U11(mark(X1),X2,X3) -> U11(X1,X2,X3) [12] U11(X1,mark(X2),X3) -> U11(X1,X2,X3) [13] U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) [14] U11(active(X1),X2,X3) -> U11(X1,X2,X3) [15] U11(X1,active(X2),X3) -> U11(X1,X2,X3) [16] U11(X1,X2,active(X3)) -> U11(X1,X2,X3) [17] U12(mark(X1),X2,X3) -> U12(X1,X2,X3) [18] U12(X1,mark(X2),X3) -> U12(X1,X2,X3) [19] U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) [20] U12(active(X1),X2,X3) -> U12(X1,X2,X3) [21] U12(X1,active(X2),X3) -> U12(X1,X2,X3) [22] U12(X1,X2,active(X3)) -> U12(X1,X2,X3) [23] s(mark(X)) -> s(X) [24] s(active(X)) -> s(X) [25] plus(mark(X1),X2) -> plus(X1,X2) [26] plus(X1,mark(X2)) -> plus(X1,X2) [27] plus(active(X1),X2) -> plus(X1,X2) [28] plus(X1,active(X2)) -> plus(X1,X2) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ mark ] (X0) = 1*X0; [ U11 ] (X0,X1,X2) = 1*X2 + 3*X1 + 3*X0; [ Marked_mark ] (X0) = 3*X0 + 2; [ tt ] () = 2; [ plus ] (X0,X1) = 3*X1 + 1*X0 + 1; [ U12 ] (X0,X1,X2) = 1*X2 + 3*X1 + 2*X0 + 1; [ s ] (X0) = 1*X0 + 3; [ Marked_active ] (X0) = 3*X0 + 2; [ active ] (X0) = 1*X0; [ 0 ] () = 0; removing < Marked_mark(s(X)),Marked_mark(X)>< Marked_mark(plus(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 [ ]} ]} ]} ]} ]} ]} Cime worked for 0.248284 seconds (real time) Cime Exit Status: 0