- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] minus(X,s(Y)) -> pred(minus(X,Y)) [2] minus(X,0) -> X [3] pred(s(X)) -> X [4] le(s(X),s(Y)) -> le(X,Y) [5] le(s(X),0) -> false [6] le(0,Y) -> true [7] gcd(0,Y) -> 0 [8] gcd(s(X),0) -> s(X) [9] gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y)) [10] if(true,s(X),s(Y)) -> gcd(minus(X,Y),s(Y)) [11] if(false,s(X),s(Y)) -> gcd(minus(Y,X),s(X)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> --> --> --> } { --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { pred(s(X)) >= X ; minus(X,s(Y)) >= pred(minus(X,Y)) ; minus(X,0) >= X ; le(s(X),s(Y)) >= le(X,Y) ; le(s(X),0) >= false ; le(0,Y) >= true ; gcd(s(X),s(Y)) >= if(le(Y,X),s(X),s(Y)) ; gcd(s(X),0) >= s(X) ; gcd(0,Y) >= 0 ; if(false,s(X),s(Y)) >= gcd(minus(Y,X),s(X)) ; if(true,s(X),s(Y)) >= gcd(minus(X,Y),s(Y)) ; Marked_if(false,s(X),s(Y)) >= Marked_gcd(minus(Y,X),s(X)) ; Marked_if(true,s(X),s(Y)) >= Marked_gcd(minus(X,Y),s(Y)) ; Marked_gcd(s(X),s(Y)) >= Marked_if(le(Y,X),s(X),s(Y)) ; } + Disjunctions:{ { Marked_if(false,s(X),s(Y)) > Marked_gcd(minus(Y,X),s(X)) ; } { Marked_if(true,s(X),s(Y)) > Marked_gcd(minus(X,Y),s(Y)) ; } { Marked_gcd(s(X),s(Y)) > Marked_if(le(Y,X),s(X),s(Y)) ; } } === 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: pred(s(X)) >= X constraint: minus(X,s(Y)) >= pred(minus(X,Y)) constraint: minus(X,0) >= X constraint: le(s(X),s(Y)) >= le(X,Y) constraint: le(s(X),0) >= false constraint: le(0,Y) >= true constraint: gcd(s(X),s(Y)) >= if(le(Y,X),s(X),s(Y)) constraint: gcd(s(X),0) >= s(X) constraint: gcd(0,Y) >= 0 constraint: if(false,s(X),s(Y)) >= gcd(minus(Y,X),s(X)) constraint: if(true,s(X),s(Y)) >= gcd(minus(X,Y),s(Y)) constraint: Marked_if(false,s(X),s(Y)) >= Marked_gcd(minus(Y,X),s(X)) constraint: Marked_if(true,s(X),s(Y)) >= Marked_gcd(minus(X,Y),s(Y)) constraint: Marked_gcd(s(X),s(Y)) >= Marked_if(le(Y,X),s(X),s(Y)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { pred(s(X)) >= X ; minus(X,s(Y)) >= pred(minus(X,Y)) ; minus(X,0) >= X ; le(s(X),s(Y)) >= le(X,Y) ; le(s(X),0) >= false ; le(0,Y) >= true ; gcd(s(X),s(Y)) >= if(le(Y,X),s(X),s(Y)) ; gcd(s(X),0) >= s(X) ; gcd(0,Y) >= 0 ; if(false,s(X),s(Y)) >= gcd(minus(Y,X),s(X)) ; if(true,s(X),s(Y)) >= gcd(minus(X,Y),s(Y)) ; Marked_le(s(X),s(Y)) >= Marked_le(X,Y) ; } + Disjunctions:{ { Marked_le(s(X),s(Y)) > Marked_le(X,Y) ; } } === 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: pred(s(X)) >= X constraint: minus(X,s(Y)) >= pred(minus(X,Y)) constraint: minus(X,0) >= X constraint: le(s(X),s(Y)) >= le(X,Y) constraint: le(s(X),0) >= false constraint: le(0,Y) >= true constraint: gcd(s(X),s(Y)) >= if(le(Y,X),s(X),s(Y)) constraint: gcd(s(X),0) >= s(X) constraint: gcd(0,Y) >= 0 constraint: if(false,s(X),s(Y)) >= gcd(minus(Y,X),s(X)) constraint: if(true,s(X),s(Y)) >= gcd(minus(X,Y),s(Y)) constraint: Marked_le(s(X),s(Y)) >= Marked_le(X,Y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { pred(s(X)) >= X ; minus(X,s(Y)) >= pred(minus(X,Y)) ; minus(X,0) >= X ; le(s(X),s(Y)) >= le(X,Y) ; le(s(X),0) >= false ; le(0,Y) >= true ; gcd(s(X),s(Y)) >= if(le(Y,X),s(X),s(Y)) ; gcd(s(X),0) >= s(X) ; gcd(0,Y) >= 0 ; if(false,s(X),s(Y)) >= gcd(minus(Y,X),s(X)) ; if(true,s(X),s(Y)) >= gcd(minus(X,Y),s(Y)) ; Marked_minus(X,s(Y)) >= Marked_minus(X,Y) ; } + Disjunctions:{ { Marked_minus(X,s(Y)) > Marked_minus(X,Y) ; } } === 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: pred(s(X)) >= X constraint: minus(X,s(Y)) >= pred(minus(X,Y)) constraint: minus(X,0) >= X constraint: le(s(X),s(Y)) >= le(X,Y) constraint: le(s(X),0) >= false constraint: le(0,Y) >= true constraint: gcd(s(X),s(Y)) >= if(le(Y,X),s(X),s(Y)) constraint: gcd(s(X),0) >= s(X) constraint: gcd(0,Y) >= 0 constraint: if(false,s(X),s(Y)) >= gcd(minus(Y,X),s(X)) constraint: if(true,s(X),s(Y)) >= gcd(minus(X,Y),s(Y)) constraint: Marked_minus(X,s(Y)) >= Marked_minus(X,Y) 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] minus(X,s(Y)) -> pred(minus(X,Y)) [2] minus(X,0) -> X [3] pred(s(X)) -> X [4] le(s(X),s(Y)) -> le(X,Y) [5] le(s(X),0) -> false [6] le(0,Y) -> true [7] gcd(0,Y) -> 0 [8] gcd(s(X),0) -> s(X) [9] gcd(s(X),s(Y)) -> if(le(Y,X),s(X),s(Y)) [10] if(true,s(X),s(Y)) -> gcd(minus(X,Y),s(Y)) [11] if(false,s(X),s(Y)) -> gcd(minus(Y,X),s(X)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ pred ] (X0) = 1*X0 + 0; [ if ] (X0,X1,X2) = 2*X1 + 1*X2 + 0; [ le ] (X0,X1) = 0; [ s ] (X0) = 3 + 2*X0 + 0; [ Marked_gcd ] (X0,X1) = 1 + 3*X0 + 2*X1 + 0; [ true ] () = 0; [ minus ] (X0,X1) = 1*X0 + 0; [ Marked_if ] (X0,X1,X2) = 2*X1 + 2*X2 + 0; [ false ] () = 0; [ 0 ] () = 0; [ gcd ] (X0,X1) = 2 + 2*X0 + 1*X1 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ pred ] (X0) = 1*X0 + 0; [ if ] (X0,X1,X2) = 2*X1 + 2*X2 + 0; [ le ] (X0,X1) = 0; [ Marked_le ] (X0,X1) = 1*X1 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ true ] () = 0; [ minus ] (X0,X1) = 1*X0 + 0; [ false ] () = 0; [ 0 ] () = 0; [ gcd ] (X0,X1) = 2 + 2*X0 + 2*X1 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ pred ] (X0) = 1*X0 + 0; [ if ] (X0,X1,X2) = 2*X1 + 1*X2 + 0; [ le ] (X0,X1) = 0; [ s ] (X0) = 1 + 2*X0 + 0; [ true ] () = 0; [ minus ] (X0,X1) = 1*X0 + 0; [ false ] () = 0; [ 0 ] () = 0; [ Marked_minus ] (X0,X1) = 3*X1 + 0; [ gcd ] (X0,X1) = 2*X0 + 1*X1 + 0; ]} ]} ]} Cime worked for 0.165599 seconds (real time) Cime Exit Status: 0