- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(0) -> 0 [2] f(s(0)) -> s(0) [3] f(s(s(x))) -> p(h(g(x))) [4] g(0) -> pair(s(0),s(0)) [5] g(s(x)) -> h(g(x)) [6] h(x) -> pair(+(p(x),q(x)),p(x)) [7] p(pair(x,y)) -> x [8] q(pair(x,y)) -> y [9] +(x,0) -> x [10] +(x,s(y)) -> s(+(x,y)) [11] f(s(s(x))) -> +(p(g(x)),q(g(x))) [12] g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(0) >= 0 ; f(s(0)) >= s(0) ; f(s(s(x))) >= p(h(g(x))) ; f(s(s(x))) >= +(p(g(x)),q(g(x))) ; p(pair(x,y)) >= x ; h(x) >= pair(+(p(x),q(x)),p(x)) ; g(0) >= pair(s(0),s(0)) ; g(s(x)) >= h(g(x)) ; g(s(x)) >= pair(+(p(g(x)),q(g(x))),p(g(x))) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; q(pair(x,y)) >= y ; Marked_g(s(x)) >= Marked_g(x) ; } + Disjunctions:{ { Marked_g(s(x)) > Marked_g(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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === STOPING TIMER virtual === constraint: f(0) >= 0 constraint: f(s(0)) >= s(0) constraint: f(s(s(x))) >= p(h(g(x))) constraint: f(s(s(x))) >= +(p(g(x)),q(g(x))) constraint: p(pair(x,y)) >= x constraint: h(x) >= pair(+(p(x),q(x)),p(x)) constraint: g(0) >= pair(s(0),s(0)) constraint: g(s(x)) >= h(g(x)) constraint: g(s(x)) >= pair(+(p(g(x)),q(g(x))),p(g(x))) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: q(pair(x,y)) >= y constraint: Marked_g(s(x)) >= Marked_g(x) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(0) >= 0 ; f(s(0)) >= s(0) ; f(s(s(x))) >= p(h(g(x))) ; f(s(s(x))) >= +(p(g(x)),q(g(x))) ; p(pair(x,y)) >= x ; h(x) >= pair(+(p(x),q(x)),p(x)) ; g(0) >= pair(s(0),s(0)) ; g(s(x)) >= h(g(x)) ; g(s(x)) >= pair(+(p(g(x)),q(g(x))),p(g(x))) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; q(pair(x,y)) >= y ; Marked_+(x,s(y)) >= Marked_+(x,y) ; } + Disjunctions:{ { Marked_+(x,s(y)) > Marked_+(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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === STOPING TIMER virtual === constraint: f(0) >= 0 constraint: f(s(0)) >= s(0) constraint: f(s(s(x))) >= p(h(g(x))) constraint: f(s(s(x))) >= +(p(g(x)),q(g(x))) constraint: p(pair(x,y)) >= x constraint: h(x) >= pair(+(p(x),q(x)),p(x)) constraint: g(0) >= pair(s(0),s(0)) constraint: g(s(x)) >= h(g(x)) constraint: g(s(x)) >= pair(+(p(g(x)),q(g(x))),p(g(x))) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: q(pair(x,y)) >= y constraint: Marked_+(x,s(y)) >= Marked_+(x,y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] f(0) -> 0 [2] f(s(0)) -> s(0) [3] f(s(s(x))) -> p(h(g(x))) [4] g(0) -> pair(s(0),s(0)) [5] g(s(x)) -> h(g(x)) [6] h(x) -> pair(+(p(x),q(x)),p(x)) [7] p(pair(x,y)) -> x [8] q(pair(x,y)) -> y [9] +(x,0) -> x [10] +(x,s(y)) -> s(+(x,y)) [11] f(s(s(x))) -> +(p(g(x)),q(g(x))) [12] g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { f > s ; f > p ; f > h ; f > g ; f > pair ; f > + ; f > q ; s < f ; s < h ; s < g ; s < + ; p < f ; p < h ; p < g ; h < f ; h > s ; h > p ; h < g ; h > pair ; h > + ; h > q ; g < f ; g > s ; g > p ; g > h ; g > pair ; g > + ; g > q ; pair < f ; pair < h ; pair < g ; + < f ; + > s ; + < h ; + < g ; q < f ; q < h ; q < g ; } ]} { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { f > s ; f > p ; f > h ; f > g ; f > pair ; f > + ; f > q ; s < f ; s < h ; s < g ; s < + ; p < f ; p < h ; p < g ; h < f ; h > s ; h > p ; h < g ; h > pair ; h > + ; h > q ; g < f ; g > s ; g > p ; g > h ; g > pair ; g > + ; g > q ; pair < f ; pair < h ; pair < g ; + < f ; + > s ; + < h ; + < g ; q < f ; q < h ; q < g ; } ]} ]} ]} Cime worked for 0.192247 seconds (real time) Cime Exit Status: 0