- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] minus(X,0) -> X [2] minus(s(X),s(Y)) -> p(minus(X,Y)) [3] p(s(X)) -> X [4] div(0,s(Y)) -> 0 [5] div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(s(X),s(Y)) >= p(minus(X,Y)) ; minus(X,0) >= X ; p(s(X)) >= X ; div(0,s(Y)) >= 0 ; div(s(X),s(Y)) >= s(div(minus(X,Y),s(Y))) ; Marked_div(s(X),s(Y)) >= Marked_div(minus(X,Y),s(Y)) ; } + Disjunctions:{ { Marked_div(s(X),s(Y)) > Marked_div(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: minus(s(X),s(Y)) >= p(minus(X,Y)) constraint: minus(X,0) >= X constraint: p(s(X)) >= X constraint: div(0,s(Y)) >= 0 constraint: div(s(X),s(Y)) >= s(div(minus(X,Y),s(Y))) constraint: Marked_div(s(X),s(Y)) >= Marked_div(minus(X,Y),s(Y)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(s(X),s(Y)) >= p(minus(X,Y)) ; minus(X,0) >= X ; p(s(X)) >= X ; div(0,s(Y)) >= 0 ; div(s(X),s(Y)) >= s(div(minus(X,Y),s(Y))) ; Marked_minus(s(X),s(Y)) >= Marked_minus(X,Y) ; } + Disjunctions:{ { Marked_minus(s(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: minus(s(X),s(Y)) >= p(minus(X,Y)) constraint: minus(X,0) >= X constraint: p(s(X)) >= X constraint: div(0,s(Y)) >= 0 constraint: div(s(X),s(Y)) >= s(div(minus(X,Y),s(Y))) constraint: Marked_minus(s(X),s(Y)) >= Marked_minus(X,Y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] minus(X,0) -> X [2] minus(s(X),s(Y)) -> p(minus(X,Y)) [3] p(s(X)) -> X [4] div(0,s(Y)) -> 0 [5] div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ minus ] (X0,X1) = 1*X0 + 0; [ div ] (X0,X1) = 2*X0 + 0; [ p ] (X0) = 2 + 1*X0 + 0; [ 0 ] () = 0; [ Marked_div ] (X0,X1) = 2*X0 + 0; [ s ] (X0) = 2 + 1*X0 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ minus ] (X0,X1) = 1*X0 + 0; [ div ] (X0,X1) = 1*X0 + 0; [ p ] (X0) = 1*X0 + 0; [ Marked_minus ] (X0,X1) = 1*X0 + 0; [ 0 ] () = 0; [ s ] (X0) = 2 + 2*X0 + 0; ]} ]} ]} Cime worked for 0.062955 seconds (real time) Cime Exit Status: 0