- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__2nd(cons1(X,cons(Y,Z))) -> mark(Y) [2] a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1))) [3] a__from(X) -> cons(mark(X),from(s(X))) [4] mark(2nd(X)) -> a__2nd(mark(X)) [5] mark(from(X)) -> a__from(mark(X)) [6] mark(cons(X1,X2)) -> cons(mark(X1),X2) [7] mark(s(X)) -> s(mark(X)) [8] mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2)) [9] a__2nd(X) -> 2nd(X) [10] a__from(X) -> from(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(cons1(X1,X2)) >= cons1(mark(X1),mark(X2)) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(from(X)) >= a__from(mark(X)) ; mark(s(X)) >= s(mark(X)) ; mark(2nd(X)) >= a__2nd(mark(X)) ; a__2nd(cons1(X,cons(Y,Z))) >= mark(Y) ; a__2nd(cons(X,X1)) >= a__2nd(cons1(mark(X),mark(X1))) ; a__2nd(X) >= 2nd(X) ; a__from(X) >= cons(mark(X),from(s(X))) ; a__from(X) >= from(X) ; Marked_a__from(X) >= Marked_mark(X) ; Marked_a__2nd(cons1(X,cons(Y,Z))) >= Marked_mark(Y) ; Marked_a__2nd(cons(X,X1)) >= Marked_a__2nd(cons1(mark(X),mark(X1))) ; Marked_a__2nd(cons(X,X1)) >= Marked_mark(X) ; Marked_a__2nd(cons(X,X1)) >= Marked_mark(X1) ; Marked_mark(cons1(X1,X2)) >= Marked_mark(X1) ; Marked_mark(cons1(X1,X2)) >= Marked_mark(X2) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; 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(2nd(X)) >= Marked_a__2nd(mark(X)) ; Marked_mark(2nd(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__from(X) > Marked_mark(X) ; } { Marked_a__2nd(cons1(X,cons(Y,Z))) > Marked_mark(Y) ; } { Marked_a__2nd(cons(X,X1)) > Marked_a__2nd(cons1(mark(X),mark(X1))) ; } { Marked_a__2nd(cons(X,X1)) > Marked_mark(X) ; } { Marked_a__2nd(cons(X,X1)) > Marked_mark(X1) ; } { Marked_mark(cons1(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(cons1(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { 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(2nd(X)) > Marked_a__2nd(mark(X)) ; } { Marked_mark(2nd(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 === 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 : 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 : 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 : 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 : 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 : 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 : 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: mark(cons1(X1,X2)) >= cons1(mark(X1),mark(X2)) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(from(X)) >= a__from(mark(X)) constraint: mark(s(X)) >= s(mark(X)) constraint: mark(2nd(X)) >= a__2nd(mark(X)) constraint: a__2nd(cons1(X,cons(Y,Z))) >= mark(Y) constraint: a__2nd(cons(X,X1)) >= a__2nd(cons1(mark(X),mark(X1))) constraint: a__2nd(X) >= 2nd(X) constraint: a__from(X) >= cons(mark(X),from(s(X))) constraint: a__from(X) >= from(X) constraint: Marked_a__from(X) >= Marked_mark(X) constraint: Marked_a__2nd(cons1(X,cons(Y,Z))) >= Marked_mark(Y) constraint: Marked_a__2nd(cons(X,X1)) >= Marked_a__2nd(cons1(mark(X),mark(X1))) constraint: Marked_a__2nd(cons(X,X1)) >= Marked_mark(X) constraint: Marked_a__2nd(cons(X,X1)) >= Marked_mark(X1) constraint: Marked_mark(cons1(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(cons1(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) 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(2nd(X)) >= Marked_a__2nd(mark(X)) constraint: Marked_mark(2nd(X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(cons1(X1,X2)) >= cons1(mark(X1),mark(X2)) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(from(X)) >= a__from(mark(X)) ; mark(s(X)) >= s(mark(X)) ; mark(2nd(X)) >= a__2nd(mark(X)) ; a__2nd(cons1(X,cons(Y,Z))) >= mark(Y) ; a__2nd(cons(X,X1)) >= a__2nd(cons1(mark(X),mark(X1))) ; a__2nd(X) >= 2nd(X) ; a__from(X) >= cons(mark(X),from(s(X))) ; a__from(X) >= from(X) ; Marked_a__from(X) >= Marked_mark(X) ; Marked_a__2nd(cons1(X,cons(Y,Z))) >= Marked_mark(Y) ; Marked_a__2nd(cons(X,X1)) >= Marked_a__2nd(cons1(mark(X),mark(X1))) ; Marked_a__2nd(cons(X,X1)) >= Marked_mark(X) ; Marked_a__2nd(cons(X,X1)) >= Marked_mark(X1) ; Marked_mark(cons1(X1,X2)) >= Marked_mark(X1) ; Marked_mark(cons1(X1,X2)) >= Marked_mark(X2) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(from(X)) >= Marked_a__from(mark(X)) ; Marked_mark(from(X)) >= Marked_mark(X) ; Marked_mark(2nd(X)) >= Marked_a__2nd(mark(X)) ; Marked_mark(2nd(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__from(X) > Marked_mark(X) ; } { Marked_a__2nd(cons1(X,cons(Y,Z))) > Marked_mark(Y) ; } { Marked_a__2nd(cons(X,X1)) > Marked_a__2nd(cons1(mark(X),mark(X1))) ; } { Marked_a__2nd(cons(X,X1)) > Marked_mark(X) ; } { Marked_a__2nd(cons(X,X1)) > Marked_mark(X1) ; } { Marked_mark(cons1(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(cons1(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(from(X)) > Marked_a__from(mark(X)) ; } { Marked_mark(from(X)) > Marked_mark(X) ; } { Marked_mark(2nd(X)) > Marked_a__2nd(mark(X)) ; } { Marked_mark(2nd(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(cons1(X1,X2)) >= cons1(mark(X1),mark(X2)) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(from(X)) >= a__from(mark(X)) constraint: mark(s(X)) >= s(mark(X)) constraint: mark(2nd(X)) >= a__2nd(mark(X)) constraint: a__2nd(cons1(X,cons(Y,Z))) >= mark(Y) constraint: a__2nd(cons(X,X1)) >= a__2nd(cons1(mark(X),mark(X1))) constraint: a__2nd(X) >= 2nd(X) constraint: a__from(X) >= cons(mark(X),from(s(X))) constraint: a__from(X) >= from(X) constraint: Marked_a__from(X) >= Marked_mark(X) constraint: Marked_a__2nd(cons1(X,cons(Y,Z))) >= Marked_mark(Y) constraint: Marked_a__2nd(cons(X,X1)) >= Marked_a__2nd(cons1(mark(X),mark(X1))) constraint: Marked_a__2nd(cons(X,X1)) >= Marked_mark(X) constraint: Marked_a__2nd(cons(X,X1)) >= Marked_mark(X1) constraint: Marked_mark(cons1(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(cons1(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(from(X)) >= Marked_a__from(mark(X)) constraint: Marked_mark(from(X)) >= Marked_mark(X) constraint: Marked_mark(2nd(X)) >= Marked_a__2nd(mark(X)) constraint: Marked_mark(2nd(X)) >= Marked_mark(X) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { mark(cons1(X1,X2)) >= cons1(mark(X1),mark(X2)) ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(from(X)) >= a__from(mark(X)) ; mark(s(X)) >= s(mark(X)) ; mark(2nd(X)) >= a__2nd(mark(X)) ; a__2nd(cons1(X,cons(Y,Z))) >= mark(Y) ; a__2nd(cons(X,X1)) >= a__2nd(cons1(mark(X),mark(X1))) ; a__2nd(X) >= 2nd(X) ; a__from(X) >= cons(mark(X),from(s(X))) ; a__from(X) >= from(X) ; Marked_a__from(X) >= Marked_mark(X) ; Marked_mark(cons1(X1,X2)) >= Marked_mark(X1) ; Marked_mark(cons1(X1,X2)) >= Marked_mark(X2) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(from(X)) >= Marked_a__from(mark(X)) ; Marked_mark(from(X)) >= Marked_mark(X) ; } + Disjunctions:{ { Marked_a__from(X) > Marked_mark(X) ; } { Marked_mark(cons1(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(cons1(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(from(X)) > Marked_a__from(mark(X)) ; } { Marked_mark(from(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(cons1(X1,X2)) >= cons1(mark(X1),mark(X2)) constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2) constraint: mark(from(X)) >= a__from(mark(X)) constraint: mark(s(X)) >= s(mark(X)) constraint: mark(2nd(X)) >= a__2nd(mark(X)) constraint: a__2nd(cons1(X,cons(Y,Z))) >= mark(Y) constraint: a__2nd(cons(X,X1)) >= a__2nd(cons1(mark(X),mark(X1))) constraint: a__2nd(X) >= 2nd(X) constraint: a__from(X) >= cons(mark(X),from(s(X))) constraint: a__from(X) >= from(X) constraint: Marked_a__from(X) >= Marked_mark(X) constraint: Marked_mark(cons1(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(cons1(X1,X2)) >= Marked_mark(X2) constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1) constraint: Marked_mark(from(X)) >= Marked_a__from(mark(X)) constraint: Marked_mark(from(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__2nd(cons1(X,cons(Y,Z))) -> mark(Y) [2] a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1))) [3] a__from(X) -> cons(mark(X),from(s(X))) [4] mark(2nd(X)) -> a__2nd(mark(X)) [5] mark(from(X)) -> a__from(mark(X)) [6] mark(cons(X1,X2)) -> cons(mark(X1),X2) [7] mark(s(X)) -> s(mark(X)) [8] mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2)) [9] a__2nd(X) -> 2nd(X) [10] a__from(X) -> from(X) , CRITERION: MDP [ { DP termination of: