- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(s(X)) -> f(X) [2] g(cons(0,Y)) -> g(Y) [3] g(cons(s(X),Y)) -> s(X) [4] h(cons(X,Y)) -> h(g(cons(X,Y))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> } { --> } { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_f -> 1 APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(s(X)) >= f(X) ; g(cons(s(X),Y)) >= s(X) ; g(cons(0,Y)) >= g(Y) ; h(cons(X,Y)) >= h(g(cons(X,Y))) ; Marked_h(cons(X,Y)) >= Marked_h(g(cons(X,Y))) ; } + Disjunctions:{ { Marked_h(cons(X,Y)) > Marked_h(g(cons(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: f(s(X)) >= f(X) constraint: g(cons(s(X),Y)) >= s(X) constraint: g(cons(0,Y)) >= g(Y) constraint: h(cons(X,Y)) >= h(g(cons(X,Y))) constraint: Marked_h(cons(X,Y)) >= Marked_h(g(cons(X,Y))) APPLY CRITERIA (Subterm criterion) ST: Marked_g -> 1 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] f(s(X)) -> f(X) [2] g(cons(0,Y)) -> g(Y) [3] g(cons(s(X),Y)) -> s(X) [4] h(cons(X,Y)) -> h(g(cons(X,Y))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ f ] (X0) = 0; [ 0 ] () = 2 + 0; [ g ] (X0) = 0; [ Marked_h ] (X0) = 3*X0 + 0; [ s ] (X0) = 0; [ h ] (X0) = 3*X0 + 0; [ cons ] (X0,X1) = 2 + 2*X0 + 2*X1 + 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.036677 seconds (real time) Cime Exit Status: 0