- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] -(x,0) -> x [2] -(0,s(y)) -> 0 [3] -(s(x),s(y)) -> -(x,y) [4] f(0) -> 0 [5] f(s(x)) -> -(s(x),g(f(x))) [6] g(0) -> s(0) [7] g(s(x)) -> -(s(x),f(g(x))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> --> --> --> --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { -(0,s(y)) >= 0 ; -(s(x),s(y)) >= -(x,y) ; -(x,0) >= x ; f(0) >= 0 ; f(s(x)) >= -(s(x),g(f(x))) ; g(0) >= s(0) ; g(s(x)) >= -(s(x),f(g(x))) ; Marked_g(s(x)) >= Marked_g(x) ; Marked_g(s(x)) >= Marked_f(g(x)) ; Marked_f(s(x)) >= Marked_g(f(x)) ; Marked_f(s(x)) >= Marked_f(x) ; } + Disjunctions:{ { Marked_g(s(x)) > Marked_g(x) ; } { Marked_g(s(x)) > Marked_f(g(x)) ; } { Marked_f(s(x)) > Marked_g(f(x)) ; } { Marked_f(s(x)) > Marked_f(x) ; } } === 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: -(0,s(y)) >= 0 constraint: -(s(x),s(y)) >= -(x,y) constraint: -(x,0) >= x constraint: f(0) >= 0 constraint: f(s(x)) >= -(s(x),g(f(x))) constraint: g(0) >= s(0) constraint: g(s(x)) >= -(s(x),f(g(x))) constraint: Marked_g(s(x)) >= Marked_g(x) constraint: Marked_g(s(x)) >= Marked_f(g(x)) constraint: Marked_f(s(x)) >= Marked_g(f(x)) constraint: Marked_f(s(x)) >= Marked_f(x) APPLY CRITERIA (Subterm criterion) ST: Marked_- -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] -(x,0) -> x [2] -(0,s(y)) -> 0 [3] -(s(x),s(y)) -> -(x,y) [4] f(0) -> 0 [5] f(s(x)) -> -(s(x),g(f(x))) [6] g(0) -> s(0) [7] g(s(x)) -> -(s(x),f(g(x))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ - ] (X0,X1) = 1 + 1*X0 + 0; [ g ] (X0) = 3 + 2*X0 + 0; [ s ] (X0) = 2 + 3*X0 + 0; [ 0 ] () = 0; [ Marked_g ] (X0) = 2 + 3*X0 + 0; [ f ] (X0) = 2*X0 + 0; [ Marked_f ] (X0) = 2*X0 + 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 0.048368 seconds (real time) Cime Exit Status: 0