- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] active(f(0)) -> mark(cons(0,f(s(0)))) [2] active(f(s(0))) -> mark(f(p(s(0)))) [3] active(p(s(X))) -> mark(X) [4] active(f(X)) -> f(active(X)) [5] active(cons(X1,X2)) -> cons(active(X1),X2) [6] active(s(X)) -> s(active(X)) [7] active(p(X)) -> p(active(X)) [8] f(mark(X)) -> mark(f(X)) [9] cons(mark(X1),X2) -> mark(cons(X1,X2)) [10] s(mark(X)) -> mark(s(X)) [11] p(mark(X)) -> mark(p(X)) [12] proper(f(X)) -> f(proper(X)) [13] proper(0) -> ok(0) [14] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) [15] proper(s(X)) -> s(proper(X)) [16] proper(p(X)) -> p(proper(X)) [17] f(ok(X)) -> ok(f(X)) [18] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) [19] s(ok(X)) -> ok(s(X)) [20] p(ok(X)) -> ok(p(X)) [21] top(mark(X)) -> top(proper(X)) [22] top(ok(X)) -> top(active(X)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 7 components: { --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { cons(mark(X1),X2) >= mark(cons(X1,X2)) ; cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ; f(mark(X)) >= mark(f(X)) ; f(ok(X)) >= ok(f(X)) ; s(mark(X)) >= mark(s(X)) ; s(ok(X)) >= ok(s(X)) ; active(cons(X1,X2)) >= cons(active(X1),X2) ; active(f(0)) >= mark(cons(0,f(s(0)))) ; active(f(s(0))) >= mark(f(p(s(0)))) ; active(f(X)) >= f(active(X)) ; active(s(X)) >= s(active(X)) ; active(p(s(X))) >= mark(X) ; active(p(X)) >= p(active(X)) ; p(mark(X)) >= mark(p(X)) ; p(ok(X)) >= ok(p(X)) ; proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ; proper(0) >= ok(0) ; proper(f(X)) >= f(proper(X)) ; proper(s(X)) >= s(proper(X)) ; proper(p(X)) >= p(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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. === TIMER virtual : 50.000000 === trying sub matrices of size: 1 Matrix interpretation constraints generated. Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. Termination constraints generated. Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 50.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: cons(mark(X1),X2) >= mark(cons(X1,X2)) constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) constraint: f(mark(X)) >= mark(f(X)) constraint: f(ok(X)) >= ok(f(X)) constraint: s(mark(X)) >= mark(s(X)) constraint: s(ok(X)) >= ok(s(X)) constraint: active(cons(X1,X2)) >= cons(active(X1),X2) constraint: active(f(0)) >= mark(cons(0,f(s(0)))) constraint: active(f(s(0))) >= mark(f(p(s(0)))) constraint: active(f(X)) >= f(active(X)) constraint: active(s(X)) >= s(active(X)) constraint: active(p(s(X))) >= mark(X) constraint: active(p(X)) >= p(active(X)) constraint: p(mark(X)) >= mark(p(X)) constraint: p(ok(X)) >= ok(p(X)) constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) constraint: proper(0) >= ok(0) constraint: proper(f(X)) >= f(proper(X)) constraint: proper(s(X)) >= s(proper(X)) constraint: proper(p(X)) >= p(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_f -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_cons -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_s -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_p -> 1 APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { cons(mark(X1),X2) >= mark(cons(X1,X2)) ; cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) ; f(mark(X)) >= mark(f(X)) ; f(ok(X)) >= ok(f(X)) ; s(mark(X)) >= mark(s(X)) ; s(ok(X)) >= ok(s(X)) ; active(cons(X1,X2)) >= cons(active(X1),X2) ; active(f(0)) >= mark(cons(0,f(s(0)))) ; active(f(s(0))) >= mark(f(p(s(0)))) ; active(f(X)) >= f(active(X)) ; active(s(X)) >= s(active(X)) ; active(p(s(X))) >= mark(X) ; active(p(X)) >= p(active(X)) ; p(mark(X)) >= mark(p(X)) ; p(ok(X)) >= ok(p(X)) ; proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) ; proper(0) >= ok(0) ; proper(f(X)) >= f(proper(X)) ; proper(s(X)) >= s(proper(X)) ; proper(p(X)) >= p(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: cons(mark(X1),X2) >= mark(cons(X1,X2)) constraint: cons(ok(X1),ok(X2)) >= ok(cons(X1,X2)) constraint: f(mark(X)) >= mark(f(X)) constraint: f(ok(X)) >= ok(f(X)) constraint: s(mark(X)) >= mark(s(X)) constraint: s(ok(X)) >= ok(s(X)) constraint: active(cons(X1,X2)) >= cons(active(X1),X2) constraint: active(f(0)) >= mark(cons(0,f(s(0)))) constraint: active(f(s(0))) >= mark(f(p(s(0)))) constraint: active(f(X)) >= f(active(X)) constraint: active(s(X)) >= s(active(X)) constraint: active(p(s(X))) >= mark(X) constraint: active(p(X)) >= p(active(X)) constraint: p(mark(X)) >= mark(p(X)) constraint: p(ok(X)) >= ok(p(X)) constraint: proper(cons(X1,X2)) >= cons(proper(X1),proper(X2)) constraint: proper(0) >= ok(0) constraint: proper(f(X)) >= f(proper(X)) constraint: proper(s(X)) >= s(proper(X)) constraint: proper(p(X)) >= p(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 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] active(f(0)) -> mark(cons(0,f(s(0)))) [2] active(f(s(0))) -> mark(f(p(s(0)))) [3] active(p(s(X))) -> mark(X) [4] active(f(X)) -> f(active(X)) [5] active(cons(X1,X2)) -> cons(active(X1),X2) [6] active(s(X)) -> s(active(X)) [7] active(p(X)) -> p(active(X)) [8] f(mark(X)) -> mark(f(X)) [9] cons(mark(X1),X2) -> mark(cons(X1,X2)) [10] s(mark(X)) -> mark(s(X)) [11] p(mark(X)) -> mark(p(X)) [12] proper(f(X)) -> f(proper(X)) [13] proper(0) -> ok(0) [14] proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) [15] proper(s(X)) -> s(proper(X)) [16] proper(p(X)) -> p(proper(X)) [17] f(ok(X)) -> ok(f(X)) [18] cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) [19] s(ok(X)) -> ok(s(X)) [20] p(ok(X)) -> ok(p(X)) [21] top(mark(X)) -> top(proper(X)) [22] top(ok(X)) -> top(active(X)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ mark ] (X0) = [ [ 1 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 1 , 1 ] ]*X0 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ ok ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ s ] (X0) = [ [ 1 , 1 , 1 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ 0 ] () = [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_top ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ p ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ cons ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ top ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ active ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ f ] (X0) = [ [ 1 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ proper ] (X0) = [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ mark ] (X0) = 0; [ ok ] (X0) = 3 + 1*X0 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ 0 ] () = 2 + 0; [ Marked_top ] (X0) = 2*X0 + 0; [ p ] (X0) = 1*X0 + 0; [ cons ] (X0,X1) = 2*X0 + 2*X1 + 0; [ top ] (X0) = 0; [ active ] (X0) = 1*X0 + 0; [ f ] (X0) = 2*X0 + 0; [ proper ] (X0) = 3*X0 + 0; ]} ]} ]} { 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 11.023048 seconds (real time) Cime Exit Status: 0