- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] fib(0) -> 0 [2] fib(s(0)) -> s(0) [3] fib(s(s(x))) -> +(fib(s(x)),fib(x)) [4] +(x,0) -> x [5] +(x,s(y)) -> s(+(x,y)) 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: { fib(0) >= 0 ; fib(s(0)) >= s(0) ; fib(s(s(x))) >= +(fib(s(x)),fib(x)) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; Marked_fib(s(s(x))) >= Marked_fib(s(x)) ; Marked_fib(s(s(x))) >= Marked_fib(x) ; } + Disjunctions:{ { Marked_fib(s(s(x))) > Marked_fib(s(x)) ; } { Marked_fib(s(s(x))) > Marked_fib(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: fib(0) >= 0 constraint: fib(s(0)) >= s(0) constraint: fib(s(s(x))) >= +(fib(s(x)),fib(x)) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: Marked_fib(s(s(x))) >= Marked_fib(s(x)) constraint: Marked_fib(s(s(x))) >= Marked_fib(x) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { fib(0) >= 0 ; fib(s(0)) >= s(0) ; fib(s(s(x))) >= +(fib(s(x)),fib(x)) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,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: fib(0) >= 0 constraint: fib(s(0)) >= s(0) constraint: fib(s(s(x))) >= +(fib(s(x)),fib(x)) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,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] fib(0) -> 0 [2] fib(s(0)) -> s(0) [3] fib(s(s(x))) -> +(fib(s(x)),fib(x)) [4] +(x,0) -> x [5] +(x,s(y)) -> s(+(x,y)) , 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.): { fib > s ; fib > + ; s < fib ; s < + ; + < fib ; + > s ; } ]} { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { fib > s ; fib > + ; s < fib ; s < + ; + < fib ; + > s ; } ]} ]} ]} Cime worked for 0.056937 seconds (real time) Cime Exit Status: 0