- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] le(0,y) -> true [2] le(s(x),0) -> false [3] le(s(x),s(y)) -> le(x,y) [4] minus(0,y) -> 0 [5] minus(s(x),y) -> if_minus(le(s(x),y),s(x),y) [6] if_minus(true,s(x),y) -> 0 [7] if_minus(false,s(x),y) -> s(minus(x,y)) [8] gcd(0,y) -> y [9] gcd(s(x),0) -> s(x) [10] gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y)) [11] if_gcd(true,s(x),s(y)) -> gcd(minus(x,y),s(y)) [12] if_gcd(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: { le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; minus(0,y) >= 0 ; minus(s(x),y) >= if_minus(le(s(x),y),s(x),y) ; if_minus(true,s(x),y) >= 0 ; if_minus(false,s(x),y) >= s(minus(x,y)) ; gcd(0,y) >= y ; gcd(s(x),0) >= s(x) ; gcd(s(x),s(y)) >= if_gcd(le(y,x),s(x),s(y)) ; if_gcd(true,s(x),s(y)) >= gcd(minus(x,y),s(y)) ; if_gcd(false,s(x),s(y)) >= gcd(minus(y,x),s(x)) ; Marked_if_gcd(true,s(x),s(y)) >= Marked_gcd(minus(x,y),s(y)) ; Marked_if_gcd(false,s(x),s(y)) >= Marked_gcd(minus(y,x),s(x)) ; Marked_gcd(s(x),s(y)) >= Marked_if_gcd(le(y,x),s(x),s(y)) ; } + Disjunctions:{ { Marked_if_gcd(true,s(x),s(y)) > Marked_gcd(minus(x,y),s(y)) ; } { Marked_if_gcd(false,s(x),s(y)) > Marked_gcd(minus(y,x),s(x)) ; } { Marked_gcd(s(x),s(y)) > Marked_if_gcd(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: le(0,y) >= true constraint: le(s(x),0) >= false constraint: le(s(x),s(y)) >= le(x,y) constraint: minus(0,y) >= 0 constraint: minus(s(x),y) >= if_minus(le(s(x),y),s(x),y) constraint: if_minus(true,s(x),y) >= 0 constraint: if_minus(false,s(x),y) >= s(minus(x,y)) constraint: gcd(0,y) >= y constraint: gcd(s(x),0) >= s(x) constraint: gcd(s(x),s(y)) >= if_gcd(le(y,x),s(x),s(y)) constraint: if_gcd(true,s(x),s(y)) >= gcd(minus(x,y),s(y)) constraint: if_gcd(false,s(x),s(y)) >= gcd(minus(y,x),s(x)) constraint: Marked_if_gcd(true,s(x),s(y)) >= Marked_gcd(minus(x,y),s(y)) constraint: Marked_if_gcd(false,s(x),s(y)) >= Marked_gcd(minus(y,x),s(x)) constraint: Marked_gcd(s(x),s(y)) >= Marked_if_gcd(le(y,x),s(x),s(y)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; minus(0,y) >= 0 ; minus(s(x),y) >= if_minus(le(s(x),y),s(x),y) ; if_minus(true,s(x),y) >= 0 ; if_minus(false,s(x),y) >= s(minus(x,y)) ; gcd(0,y) >= y ; gcd(s(x),0) >= s(x) ; gcd(s(x),s(y)) >= if_gcd(le(y,x),s(x),s(y)) ; if_gcd(true,s(x),s(y)) >= gcd(minus(x,y),s(y)) ; if_gcd(false,s(x),s(y)) >= gcd(minus(y,x),s(x)) ; Marked_minus(s(x),y) >= Marked_if_minus(le(s(x),y),s(x),y) ; Marked_if_minus(false,s(x),y) >= Marked_minus(x,y) ; } + Disjunctions:{ { Marked_minus(s(x),y) > Marked_if_minus(le(s(x),y),s(x),y) ; } { Marked_if_minus(false,s(x),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: le(0,y) >= true constraint: le(s(x),0) >= false constraint: le(s(x),s(y)) >= le(x,y) constraint: minus(0,y) >= 0 constraint: minus(s(x),y) >= if_minus(le(s(x),y),s(x),y) constraint: if_minus(true,s(x),y) >= 0 constraint: if_minus(false,s(x),y) >= s(minus(x,y)) constraint: gcd(0,y) >= y constraint: gcd(s(x),0) >= s(x) constraint: gcd(s(x),s(y)) >= if_gcd(le(y,x),s(x),s(y)) constraint: if_gcd(true,s(x),s(y)) >= gcd(minus(x,y),s(y)) constraint: if_gcd(false,s(x),s(y)) >= gcd(minus(y,x),s(x)) constraint: Marked_minus(s(x),y) >= Marked_if_minus(le(s(x),y),s(x),y) constraint: Marked_if_minus(false,s(x),y) >= Marked_minus(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; minus(0,y) >= 0 ; minus(s(x),y) >= if_minus(le(s(x),y),s(x),y) ; if_minus(true,s(x),y) >= 0 ; if_minus(false,s(x),y) >= s(minus(x,y)) ; gcd(0,y) >= y ; gcd(s(x),0) >= s(x) ; gcd(s(x),s(y)) >= if_gcd(le(y,x),s(x),s(y)) ; if_gcd(true,s(x),s(y)) >= gcd(minus(x,y),s(y)) ; if_gcd(false,s(x),s(y)) >= gcd(minus(y,x),s(x)) ; 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: le(0,y) >= true constraint: le(s(x),0) >= false constraint: le(s(x),s(y)) >= le(x,y) constraint: minus(0,y) >= 0 constraint: minus(s(x),y) >= if_minus(le(s(x),y),s(x),y) constraint: if_minus(true,s(x),y) >= 0 constraint: if_minus(false,s(x),y) >= s(minus(x,y)) constraint: gcd(0,y) >= y constraint: gcd(s(x),0) >= s(x) constraint: gcd(s(x),s(y)) >= if_gcd(le(y,x),s(x),s(y)) constraint: if_gcd(true,s(x),s(y)) >= gcd(minus(x,y),s(y)) constraint: if_gcd(false,s(x),s(y)) >= gcd(minus(y,x),s(x)) constraint: Marked_le(s(x),s(y)) >= Marked_le(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] le(0,y) -> true [2] le(s(x),0) -> false [3] le(s(x),s(y)) -> le(x,y) [4] minus(0,y) -> 0 [5] minus(s(x),y) -> if_minus(le(s(x),y),s(x),y) [6] if_minus(true,s(x),y) -> 0 [7] if_minus(false,s(x),y) -> s(minus(x,y)) [8] gcd(0,y) -> y [9] gcd(s(x),0) -> s(x) [10] gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y)) [11] if_gcd(true,s(x),s(y)) -> gcd(minus(x,y),s(y)) [12] if_gcd(false,s(x),s(y)) -> gcd(minus(y,x),s(x)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ true ] () = 0; [ if_gcd ] (X0,X1,X2) = 1*X2 + 2*X1; [ s ] (X0) = 2*X0 + 2; [ 0 ] () = 0; [ Marked_gcd ] (X0,X1) = 1*X1 + 2*X0 + 2; [ if_minus ] (X0,X1,X2) = 1*X1; [ le ] (X0,X1) = 0; [ Marked_if_gcd ] (X0,X1,X2) = 1*X2 + 1*X1; [ minus ] (X0,X1) = 1*X0; [ false ] () = 0; [ gcd ] (X0,X1) = 1*X1 + 2*X0; removing [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ true ] () = 0; [ if_gcd ] (X0,X1,X2) = 1*X2 + 1*X1; [ s ] (X0) = 2*X0 + 2; [ 0 ] () = 0; [ if_minus ] (X0,X1,X2) = 1*X1; [ le ] (X0,X1) = 0; [ minus ] (X0,X1) = 1*X0; [ Marked_if_minus ] (X0,X1,X2) = 3*X2 + 1*X1; [ false ] () = 0; [ Marked_minus ] (X0,X1) = 3*X1 + 1*X0; [ gcd ] (X0,X1) = 1*X1 + 1*X0; removing [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ true ] () = 0; [ if_gcd ] (X0,X1,X2) = 2 + 1*X1 + 1*X2 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ Marked_le ] (X0,X1) = 1*X1 + 0; [ 0 ] () = 0; [ if_minus ] (X0,X1,X2) = 1*X1 + 0; [ le ] (X0,X1) = 0; [ minus ] (X0,X1) = 1*X0 + 0; [ false ] () = 0; [ gcd ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; ]} ]} ]} Cime worked for 0.251115 seconds (real time) Cime Exit Status: 0