- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z)) [2] plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { plus(s(X),plus(Y,Z)) >= plus(X,plus(s(s(Y)),Z)) ; plus(s(X1),plus(X2,plus(X3,X4))) >= plus(X1,plus(X3,plus(X2,X4))) ; Marked_plus(s(X),plus(Y,Z)) >= Marked_plus(s(s(Y)),Z) ; Marked_plus(s(X),plus(Y,Z)) >= Marked_plus(X,plus(s(s(Y)),Z)) ; Marked_plus(s(X1),plus(X2,plus(X3,X4))) >= Marked_plus(X1, plus(X3,plus(X2,X4))) ; Marked_plus(s(X1),plus(X2,plus(X3,X4))) >= Marked_plus(X2,X4) ; Marked_plus(s(X1),plus(X2,plus(X3,X4))) >= Marked_plus(X3,plus(X2,X4)) ; } + Disjunctions:{ { Marked_plus(s(X),plus(Y,Z)) > Marked_plus(s(s(Y)),Z) ; } { Marked_plus(s(X),plus(Y,Z)) > Marked_plus(X,plus(s(s(Y)),Z)) ; } { Marked_plus(s(X1),plus(X2,plus(X3,X4))) > Marked_plus(X1, plus(X3,plus(X2,X4))) ; } { Marked_plus(s(X1),plus(X2,plus(X3,X4))) > Marked_plus(X2,X4) ; } { Marked_plus(s(X1),plus(X2,plus(X3,X4))) > Marked_plus(X3,plus(X2,X4)) ; } } === 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(s(X),plus(Y,Z)) >= plus(X,plus(s(s(Y)),Z)) constraint: plus(s(X1),plus(X2,plus(X3,X4))) >= plus(X1,plus(X3,plus(X2,X4))) constraint: Marked_plus(s(X),plus(Y,Z)) >= Marked_plus(s(s(Y)),Z) constraint: Marked_plus(s(X),plus(Y,Z)) >= Marked_plus(X,plus(s(s(Y)),Z)) constraint: Marked_plus(s(X1),plus(X2,plus(X3,X4))) >= Marked_plus(X1, plus(X3,plus(X2,X4))) constraint: Marked_plus(s(X1),plus(X2,plus(X3,X4))) >= Marked_plus(X2,X4) constraint: Marked_plus(s(X1),plus(X2,plus(X3,X4))) >= Marked_plus(X3, plus(X2,X4)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_plus -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z)) [2] plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ plus ] (X0,X1) = 2*X1 + 2; [ Marked_plus ] (X0,X1) = 2*X1; [ s ] (X0) = 0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} Cime worked for 0.059966 seconds (real time) Cime Exit Status: 0