- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] plus(0,Y) -> Y [2] plus(s(X),Y) -> s(plus(X,Y)) [3] min(X,0) -> X [4] min(s(X),s(Y)) -> min(X,Y) [5] min(min(X,Y),Z) -> min(X,plus(Y,Z)) [6] quot(0,s(Y)) -> 0 [7] quot(s(X),s(Y)) -> s(quot(min(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: { plus(0,Y) >= Y ; plus(s(X),Y) >= s(plus(X,Y)) ; min(s(X),s(Y)) >= min(X,Y) ; min(min(X,Y),Z) >= min(X,plus(Y,Z)) ; min(X,0) >= X ; quot(0,s(Y)) >= 0 ; quot(s(X),s(Y)) >= s(quot(min(X,Y),s(Y))) ; Marked_quot(s(X),s(Y)) >= Marked_quot(min(X,Y),s(Y)) ; } + Disjunctions:{ { Marked_quot(s(X),s(Y)) > Marked_quot(min(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: plus(0,Y) >= Y constraint: plus(s(X),Y) >= s(plus(X,Y)) constraint: min(s(X),s(Y)) >= min(X,Y) constraint: min(min(X,Y),Z) >= min(X,plus(Y,Z)) constraint: min(X,0) >= X constraint: quot(0,s(Y)) >= 0 constraint: quot(s(X),s(Y)) >= s(quot(min(X,Y),s(Y))) constraint: Marked_quot(s(X),s(Y)) >= Marked_quot(min(X,Y),s(Y)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { plus(0,Y) >= Y ; plus(s(X),Y) >= s(plus(X,Y)) ; min(s(X),s(Y)) >= min(X,Y) ; min(min(X,Y),Z) >= min(X,plus(Y,Z)) ; min(X,0) >= X ; quot(0,s(Y)) >= 0 ; quot(s(X),s(Y)) >= s(quot(min(X,Y),s(Y))) ; Marked_min(s(X),s(Y)) >= Marked_min(X,Y) ; Marked_min(min(X,Y),Z) >= Marked_min(X,plus(Y,Z)) ; } + Disjunctions:{ { Marked_min(s(X),s(Y)) > Marked_min(X,Y) ; } { Marked_min(min(X,Y),Z) > Marked_min(X,plus(Y,Z)) ; } } === 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: plus(0,Y) >= Y constraint: plus(s(X),Y) >= s(plus(X,Y)) constraint: min(s(X),s(Y)) >= min(X,Y) constraint: min(min(X,Y),Z) >= min(X,plus(Y,Z)) constraint: min(X,0) >= X constraint: quot(0,s(Y)) >= 0 constraint: quot(s(X),s(Y)) >= s(quot(min(X,Y),s(Y))) constraint: Marked_min(s(X),s(Y)) >= Marked_min(X,Y) constraint: Marked_min(min(X,Y),Z) >= Marked_min(X,plus(Y,Z)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { plus(0,Y) >= Y ; plus(s(X),Y) >= s(plus(X,Y)) ; min(s(X),s(Y)) >= min(X,Y) ; min(min(X,Y),Z) >= min(X,plus(Y,Z)) ; min(X,0) >= X ; quot(0,s(Y)) >= 0 ; quot(s(X),s(Y)) >= s(quot(min(X,Y),s(Y))) ; Marked_plus(s(X),Y) >= Marked_plus(X,Y) ; } + Disjunctions:{ { Marked_plus(s(X),Y) > Marked_plus(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: plus(0,Y) >= Y constraint: plus(s(X),Y) >= s(plus(X,Y)) constraint: min(s(X),s(Y)) >= min(X,Y) constraint: min(min(X,Y),Z) >= min(X,plus(Y,Z)) constraint: min(X,0) >= X constraint: quot(0,s(Y)) >= 0 constraint: quot(s(X),s(Y)) >= s(quot(min(X,Y),s(Y))) constraint: Marked_plus(s(X),Y) >= Marked_plus(X,Y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { plus(0,Y) >= Y ; plus(s(X),Y) >= s(plus(X,Y)) ; min(s(X),s(Y)) >= min(X,Y) ; min(min(X,Y),Z) >= min(X,plus(Y,Z)) ; min(X,0) >= X ; quot(0,s(Y)) >= 0 ; quot(s(X),s(Y)) >= s(quot(min(X,Y),s(Y))) ; Marked_min(s(X),s(Y)) >= Marked_min(X,Y) ; } + Disjunctions:{ { Marked_min(s(X),s(Y)) > Marked_min(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: plus(0,Y) >= Y constraint: plus(s(X),Y) >= s(plus(X,Y)) constraint: min(s(X),s(Y)) >= min(X,Y) constraint: min(min(X,Y),Z) >= min(X,plus(Y,Z)) constraint: min(X,0) >= X constraint: quot(0,s(Y)) >= 0 constraint: quot(s(X),s(Y)) >= s(quot(min(X,Y),s(Y))) constraint: Marked_min(s(X),s(Y)) >= Marked_min(X,Y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] plus(0,Y) -> Y [2] plus(s(X),Y) -> s(plus(X,Y)) [3] min(X,0) -> X [4] min(s(X),s(Y)) -> min(X,Y) [5] min(min(X,Y),Z) -> min(X,plus(Y,Z)) [6] quot(0,s(Y)) -> 0 [7] quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ plus ] (X0,X1) = 2*X0 + 2*X1 + 0; [ Z ] () = 0; [ s ] (X0) = 2 + 1*X0 + 0; [ Marked_quot ] (X0,X1) = 2*X0 + 0; [ 0 ] () = 0; [ quot ] (X0,X1) = 1*X0 + 0; [ min ] (X0,X1) = 1*X0 + 0; ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ plus ] (X0,X1) = 2*X1 + 1*X0 + 1; [ Z ] () = 0; [ s ] (X0) = 1*X0; [ 0 ] () = 0; [ quot ] (X0,X1) = 0; [ min ] (X0,X1) = 2*X1 + 2*X0 + 2; [ Marked_min ] (X0,X1) = 3*X1 + 2*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ plus ] (X0,X1) = 1*X0 + 1*X1 + 0; [ Z ] () = 0; [ s ] (X0) = 2 + 1*X0 + 0; [ 0 ] () = 0; [ quot ] (X0,X1) = 2*X0 + 0; [ min ] (X0,X1) = 1*X0 + 0; [ Marked_min ] (X0,X1) = 2*X0 + 0; ]} ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ plus ] (X0,X1) = 2*X0 + 2*X1 + 0; [ Marked_plus ] (X0,X1) = 3*X0 + 0; [ Z ] () = 0; [ s ] (X0) = 2 + 1*X0 + 0; [ 0 ] () = 0; [ quot ] (X0,X1) = 1*X0 + 0; [ min ] (X0,X1) = 1*X0 + 0; ]} ]} ]} Cime worked for 0.172113 seconds (real time) Cime Exit Status: 0