- : 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) -> ifMinus(le(s(X),Y),s(X),Y) [6] ifMinus(true,s(X),Y) -> 0 [7] ifMinus(false,s(X),Y) -> s(minus(X,Y)) [8] quot(0,s(Y)) -> 0 [9] quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) 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) >= ifMinus(le(s(X),Y),s(X),Y) ; ifMinus(true,s(X),Y) >= 0 ; ifMinus(false,s(X),Y) >= s(minus(X,Y)) ; quot(0,s(Y)) >= 0 ; quot(s(X),s(Y)) >= s(quot(minus(X,Y),s(Y))) ; Marked_quot(s(X),s(Y)) >= Marked_quot(minus(X,Y),s(Y)) ; } + Disjunctions:{ { Marked_quot(s(X),s(Y)) > Marked_quot(minus(X,Y),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) >= ifMinus(le(s(X),Y),s(X),Y) constraint: ifMinus(true,s(X),Y) >= 0 constraint: ifMinus(false,s(X),Y) >= s(minus(X,Y)) constraint: quot(0,s(Y)) >= 0 constraint: quot(s(X),s(Y)) >= s(quot(minus(X,Y),s(Y))) constraint: Marked_quot(s(X),s(Y)) >= Marked_quot(minus(X,Y),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) >= ifMinus(le(s(X),Y),s(X),Y) ; ifMinus(true,s(X),Y) >= 0 ; ifMinus(false,s(X),Y) >= s(minus(X,Y)) ; quot(0,s(Y)) >= 0 ; quot(s(X),s(Y)) >= s(quot(minus(X,Y),s(Y))) ; Marked_minus(s(X),Y) >= Marked_ifMinus(le(s(X),Y),s(X),Y) ; Marked_ifMinus(false,s(X),Y) >= Marked_minus(X,Y) ; } + Disjunctions:{ { Marked_minus(s(X),Y) > Marked_ifMinus(le(s(X),Y),s(X),Y) ; } { Marked_ifMinus(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) >= ifMinus(le(s(X),Y),s(X),Y) constraint: ifMinus(true,s(X),Y) >= 0 constraint: ifMinus(false,s(X),Y) >= s(minus(X,Y)) constraint: quot(0,s(Y)) >= 0 constraint: quot(s(X),s(Y)) >= s(quot(minus(X,Y),s(Y))) constraint: Marked_minus(s(X),Y) >= Marked_ifMinus(le(s(X),Y),s(X),Y) constraint: Marked_ifMinus(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) >= ifMinus(le(s(X),Y),s(X),Y) ; ifMinus(true,s(X),Y) >= 0 ; ifMinus(false,s(X),Y) >= s(minus(X,Y)) ; quot(0,s(Y)) >= 0 ; quot(s(X),s(Y)) >= s(quot(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: 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) >= ifMinus(le(s(X),Y),s(X),Y) constraint: ifMinus(true,s(X),Y) >= 0 constraint: ifMinus(false,s(X),Y) >= s(minus(X,Y)) constraint: quot(0,s(Y)) >= 0 constraint: quot(s(X),s(Y)) >= s(quot(minus(X,Y),s(Y))) 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) -> ifMinus(le(s(X),Y),s(X),Y) [6] ifMinus(true,s(X),Y) -> 0 [7] ifMinus(false,s(X),Y) -> s(minus(X,Y)) [8] quot(0,s(Y)) -> 0 [9] quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ true ] () = 0; [ Marked_quot ] (X0,X1) = 3*X0 + 0; [ s ] (X0) = 2 + 2*X0 + 0; [ 0 ] () = 0; [ ifMinus ] (X0,X1,X2) = 1*X1 + 0; [ le ] (X0,X1) = 0; [ minus ] (X0,X1) = 1*X0 + 0; [ false ] () = 0; [ quot ] (X0,X1) = 1*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ true ] () = 0; [ s ] (X0) = 1 + 2*X0 + 0; [ 0 ] () = 0; [ Marked_ifMinus ] (X0,X1,X2) = 2*X1 + 3*X2 + 0; [ ifMinus ] (X0,X1,X2) = 1*X1 + 0; [ le ] (X0,X1) = 0; [ Marked_minus ] (X0,X1) = 1 + 3*X0 + 3*X1 + 0; [ minus ] (X0,X1) = 1*X0 + 0; [ false ] () = 0; [ quot ] (X0,X1) = 1*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ true ] () = 0; [ s ] (X0) = 1 + 2*X0 + 0; [ 0 ] () = 0; [ ifMinus ] (X0,X1,X2) = 1*X1 + 0; [ le ] (X0,X1) = 0; [ minus ] (X0,X1) = 1*X0 + 0; [ false ] () = 0; [ Marked_le ] (X0,X1) = 1*X0 + 0; [ quot ] (X0,X1) = 1*X0 + 0; ]} ]} ]} Cime worked for 0.169946 seconds (real time) Cime Exit Status: 0