- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] +(x,0) -> x [2] +(x,s(y)) -> s(+(x,y)) [3] +(0,y) -> y [4] +(s(x),y) -> s(+(x,y)) [5] +(x,+(y,z)) -> +(+(x,y),z) [6] f(g(f(x))) -> f(h(s(0),x)) [7] f(g(h(x,y))) -> f(h(s(x),y)) [8] f(h(x,h(y,z))) -> f(h(+(x,y),z)) 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,y) >= y ; +(s(x),y) >= s(+(x,y)) ; +(x,+(y,z)) >= +(+(x,y),z) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; f(h(x,h(y,z))) >= f(h(+(x,y),z)) ; f(g(f(x))) >= f(h(s(0),x)) ; f(g(h(x,y))) >= f(h(s(x),y)) ; Marked_f(h(x,h(y,z))) >= Marked_f(h(+(x,y),z)) ; } + Disjunctions:{ { Marked_f(h(x,h(y,z))) > Marked_f(h(+(x,y),z)) ; } } === 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,y) >= y constraint: +(s(x),y) >= s(+(x,y)) constraint: +(x,+(y,z)) >= +(+(x,y),z) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: f(h(x,h(y,z))) >= f(h(+(x,y),z)) constraint: f(g(f(x))) >= f(h(s(0),x)) constraint: f(g(h(x,y))) >= f(h(s(x),y)) constraint: Marked_f(h(x,h(y,z))) >= Marked_f(h(+(x,y),z)) APPLY CRITERIA (Subterm criterion) ST: Marked_+ -> 2 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_+ -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] +(x,0) -> x [2] +(x,s(y)) -> s(+(x,y)) [3] +(0,y) -> y [4] +(s(x),y) -> s(+(x,y)) [5] +(x,+(y,z)) -> +(+(x,y),z) [6] f(g(f(x))) -> f(h(s(0),x)) [7] f(g(h(x,y))) -> f(h(s(x),y)) [8] f(h(x,h(y,z))) -> f(h(+(x,y),z)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ + ] (X0,X1) = 1 + 1*X0 + 2*X1 + 0; [ h ] (X0,X1) = 2 + 3*X1 + 0; [ s ] (X0) = 0; [ Marked_f ] (X0) = 1*X0 + 0; [ 0 ] () = 0; [ g ] (X0) = 2 + 3*X0 + 0; [ f ] (X0) = 3*X0 + 0; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} Cime worked for 0.067928 seconds (real time) Cime Exit Status: 0