- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__f(0) -> cons(0,f(s(0))) [2] a__f(s(0)) -> a__f(a__p(s(0))) [3] a__p(s(X)) -> mark(X) [4] mark(f(X)) -> a__f(mark(X)) [5] mark(p(X)) -> a__p(mark(X)) [6] mark(0) -> 0 [7] mark(cons(X1,X2)) -> cons(mark(X1),X2) [8] mark(s(X)) -> s(mark(X)) [9] a__f(X) -> f(X) [10] a__p(X) -> p(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__f(0) >= cons(0,f(s(0))) ; a__f(s(0)) >= a__f(a__p(s(0))) ; a__f(X) >= f(X) ; a__p(s(X)) >= mark(X) ; a__p(X) >= p(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(f(X)) >= a__f(mark(X)) ; mark(s(X)) >= s(mark(X)) ; mark(p(X)) >= a__p(mark(X)) ; Marked_a__p(s(X)) >= Marked_mark(X) ; Marked_a__f(s(0)) >= Marked_a__p(s(0)) ; Marked_a__f(s(0)) >= Marked_a__f(a__p(s(0))) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(f(X)) >= Marked_a__f(mark(X)) ; Marked_mark(f(X)) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(p(X)) >= Marked_a__p(mark(X)) ; Marked_mark(p(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__p(s(X)) > Marked_mark(X) ; } { Marked_a__f(s(0)) > Marked_a__p(s(0)) ; } { Marked_a__f(s(0)) > Marked_a__f(a__p(s(0))) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(f(X)) > Marked_a__f(mark(X)) ; } { Marked_mark(f(X)) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(p(X)) > Marked_a__p(mark(X)) ; } { Marked_mark(p(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__f(0) >= cons(0,f(s(0))) constraint: a__f(s(0)) >= a__f(a__p(s(0))) constraint: a__f(X) >= f(X) constraint: a__p(s(X)) >= mark(X) constraint: a__p(X) >= p(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(f(X)) >= a__f(mark(X)) constraint: mark(s(X)) >= s(mark(X)) constraint: mark(p(X)) >= a__p(mark(X)) constraint: Marked_a__p(s(X)) >= Marked_mark(X) constraint: Marked_a__f(s(0)) >= Marked_a__p(s(0)) constraint: Marked_a__f(s(0)) >= Marked_a__f(a__p(s(0))) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(f(X)) >= Marked_a__f(mark(X)) constraint: Marked_mark(f(X)) >= Marked_mark(X) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(p(X)) >= Marked_a__p(mark(X)) constraint: Marked_mark(p(X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__f(0) >= cons(0,f(s(0))) ; a__f(s(0)) >= a__f(a__p(s(0))) ; a__f(X) >= f(X) ; a__p(s(X)) >= mark(X) ; a__p(X) >= p(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(f(X)) >= a__f(mark(X)) ; mark(s(X)) >= s(mark(X)) ; mark(p(X)) >= a__p(mark(X)) ; Marked_a__p(s(X)) >= Marked_mark(X) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(p(X)) >= Marked_a__p(mark(X)) ; Marked_mark(p(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__p(s(X)) > Marked_mark(X) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(p(X)) > Marked_a__p(mark(X)) ; } { Marked_mark(p(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__f(0) >= cons(0,f(s(0))) constraint: a__f(s(0)) >= a__f(a__p(s(0))) constraint: a__f(X) >= f(X) constraint: a__p(s(X)) >= mark(X) constraint: a__p(X) >= p(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(f(X)) >= a__f(mark(X)) constraint: mark(s(X)) >= s(mark(X)) constraint: mark(p(X)) >= a__p(mark(X)) constraint: Marked_a__p(s(X)) >= Marked_mark(X) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(s(X)) >= Marked_mark(X) constraint: Marked_mark(p(X)) >= Marked_a__p(mark(X)) constraint: Marked_mark(p(X)) >= Marked_mark(X) APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__f(0) >= cons(0,f(s(0))) ; a__f(s(0)) >= a__f(a__p(s(0))) ; a__f(X) >= f(X) ; a__p(s(X)) >= mark(X) ; a__p(X) >= p(X) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(0) >= 0 ; mark(f(X)) >= a__f(mark(X)) ; mark(s(X)) >= s(mark(X)) ; mark(p(X)) >= a__p(mark(X)) ; Marked_a__f(s(0)) >= Marked_a__f(a__p(s(0))) ; } + Disjunctions:{ { Marked_a__f(s(0)) > Marked_a__f(a__p(s(0))) ; } } === 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 : 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: a__f(0) >= cons(0,f(s(0))) constraint: a__f(s(0)) >= a__f(a__p(s(0))) constraint: a__f(X) >= f(X) constraint: a__p(s(X)) >= mark(X) constraint: a__p(X) >= p(X) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(0) >= 0 constraint: mark(f(X)) >= a__f(mark(X)) constraint: mark(s(X)) >= s(mark(X)) constraint: mark(p(X)) >= a__p(mark(X)) constraint: Marked_a__f(s(0)) >= Marked_a__f(a__p(s(0))) 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 0 components: SOLVED { TRS termination of: [1] a__f(0) -> cons(0,f(s(0))) [2] a__f(s(0)) -> a__f(a__p(s(0))) [3] a__p(s(X)) -> mark(X) [4] mark(f(X)) -> a__f(mark(X)) [5] mark(p(X)) -> a__p(mark(X)) [6] mark(0) -> 0 [7] mark(cons(X1,X2)) -> cons(mark(X1),X2) [8] mark(s(X)) -> s(mark(X)) [9] a__f(X) -> f(X) [10] a__p(X) -> p(X) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ cons ] (X0,X1) = 1*X0; [ Marked_a__p ] (X0) = 2*X0; [ a__f ] (X0) = 2*X0 + 2; [ f ] (X0) = 2*X0 + 1; [ Marked_mark ] (X0) = 2*X0; [ mark ] (X0) = 2*X0; [ 0 ] () = 0; [ Marked_a__f ] (X0) = 2; [ a__p ] (X0) = 2*X0; [ s ] (X0) = 2*X0; [ p ] (X0) = 2*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ cons ] (X0,X1) = 1*X0; [ Marked_a__p ] (X0) = 3*X0 + 3; [ a__f ] (X0) = 3; [ f ] (X0) = 3; [ Marked_mark ] (X0) = 3*X0 + 2; [ mark ] (X0) = 1*X0 + 1; [ 0 ] () = 0; [ a__p ] (X0) = 1*X0 + 2; [ s ] (X0) = 1*X0 + 2; [ p ] (X0) = 1*X0 + 2; removing < Marked_mark(p(X)),Marked_mark(X)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ cons ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ a__f ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ f ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ mark ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ 0 ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; [ Marked_a__f ] (X0) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ a__p ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ s ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ p ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; ]} ]} ]} ]} ]} Cime worked for 1.071327 seconds (real time) Cime Exit Status: 0