- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(a,a) -> f(a,b) [2] f(a,b) -> f(s(a),c) [3] f(s(X),c) -> f(X,c) [4] f(c,c) -> f(a,a) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(a,a) >= f(a,b) ; f(a,b) >= f(s(a),c) ; f(s(X),c) >= f(X,c) ; f(c,c) >= f(a,a) ; Marked_f(a,a) >= Marked_f(a,b) ; Marked_f(a,b) >= Marked_f(s(a),c) ; Marked_f(s(X),c) >= Marked_f(X,c) ; Marked_f(c,c) >= Marked_f(a,a) ; } + Disjunctions:{ { Marked_f(a,a) > Marked_f(a,b) ; } { Marked_f(a,b) > Marked_f(s(a),c) ; } { Marked_f(s(X),c) > Marked_f(X,c) ; } { Marked_f(c,c) > Marked_f(a,a) ; } } === 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: f(a,a) >= f(a,b) constraint: f(a,b) >= f(s(a),c) constraint: f(s(X),c) >= f(X,c) constraint: f(c,c) >= f(a,a) constraint: Marked_f(a,a) >= Marked_f(a,b) constraint: Marked_f(a,b) >= Marked_f(s(a),c) constraint: Marked_f(s(X),c) >= Marked_f(X,c) constraint: Marked_f(c,c) >= Marked_f(a,a) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(a,a) >= f(a,b) ; f(a,b) >= f(s(a),c) ; f(s(X),c) >= f(X,c) ; f(c,c) >= f(a,a) ; Marked_f(s(X),c) >= Marked_f(X,c) ; } + Disjunctions:{ { Marked_f(s(X),c) > Marked_f(X,c) ; } } === 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: f(a,a) >= f(a,b) constraint: f(a,b) >= f(s(a),c) constraint: f(s(X),c) >= f(X,c) constraint: f(c,c) >= f(a,a) constraint: Marked_f(s(X),c) >= Marked_f(X,c) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(a,a) -> f(a,b) [2] f(a,b) -> f(s(a),c) [3] f(s(X),c) -> f(X,c) [4] f(c,c) -> f(a,a) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ f ] (X0,X1) = 0; [ c ] () = 1; [ b ] () = 0; [ a ] () = 0; [ Marked_f ] (X0,X1) = 2*X0; [ s ] (X0) = 1*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ f ] (X0,X1) = 0; [ c ] () = 0; [ b ] () = 0; [ a ] () = 0; [ Marked_f ] (X0,X1) = 3*X0 + 0; [ s ] (X0) = 2 + 2*X0 + 0; ]} ]} ]} ]} ]} Cime worked for 0.047024 seconds (real time) Cime Exit Status: 0