- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] sqr(0) -> 0 [2] sqr(s(x)) -> +(sqr(x),s(double(x))) [3] double(0) -> 0 [4] double(s(x)) -> s(s(double(x))) [5] +(x,0) -> x [6] +(x,s(y)) -> s(+(x,y)) [7] sqr(s(x)) -> s(+(sqr(x),double(x))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> --> --> --> } { --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { sqr(0) >= 0 ; sqr(s(x)) >= +(sqr(x),s(double(x))) ; sqr(s(x)) >= s(+(sqr(x),double(x))) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; double(0) >= 0 ; double(s(x)) >= s(s(double(x))) ; Marked_sqr(s(x)) >= Marked_sqr(x) ; } + Disjunctions:{ { Marked_sqr(s(x)) > Marked_sqr(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: sqr(0) >= 0 constraint: sqr(s(x)) >= +(sqr(x),s(double(x))) constraint: sqr(s(x)) >= s(+(sqr(x),double(x))) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: double(0) >= 0 constraint: double(s(x)) >= s(s(double(x))) constraint: Marked_sqr(s(x)) >= Marked_sqr(x) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { sqr(0) >= 0 ; sqr(s(x)) >= +(sqr(x),s(double(x))) ; sqr(s(x)) >= s(+(sqr(x),double(x))) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; double(0) >= 0 ; double(s(x)) >= s(s(double(x))) ; 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: sqr(0) >= 0 constraint: sqr(s(x)) >= +(sqr(x),s(double(x))) constraint: sqr(s(x)) >= s(+(sqr(x),double(x))) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: double(0) >= 0 constraint: double(s(x)) >= s(s(double(x))) constraint: Marked_+(x,s(y)) >= Marked_+(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { sqr(0) >= 0 ; sqr(s(x)) >= +(sqr(x),s(double(x))) ; sqr(s(x)) >= s(+(sqr(x),double(x))) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; double(0) >= 0 ; double(s(x)) >= s(s(double(x))) ; Marked_double(s(x)) >= Marked_double(x) ; } + Disjunctions:{ { Marked_double(s(x)) > Marked_double(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: sqr(0) >= 0 constraint: sqr(s(x)) >= +(sqr(x),s(double(x))) constraint: sqr(s(x)) >= s(+(sqr(x),double(x))) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: double(0) >= 0 constraint: double(s(x)) >= s(s(double(x))) constraint: Marked_double(s(x)) >= Marked_double(x) 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] sqr(0) -> 0 [2] sqr(s(x)) -> +(sqr(x),s(double(x))) [3] double(0) -> 0 [4] double(s(x)) -> s(s(double(x))) [5] +(x,0) -> x [6] +(x,s(y)) -> s(+(x,y)) [7] sqr(s(x)) -> s(+(sqr(x),double(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.): { sqr > + ; sqr > s ; sqr > double ; + < sqr ; + > s ; s < sqr ; s < + ; s < double ; double < sqr ; double > s ; } ]} { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { sqr > + ; sqr > s ; sqr > double ; + < sqr ; + > s ; s < sqr ; s < + ; s < double ; double < sqr ; double > s ; } ]} { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { sqr > + ; sqr > s ; sqr > double ; + < sqr ; + > s ; s < sqr ; s < + ; s < double ; double < sqr ; double > s ; } ]} ]} ]} Cime worked for 0.110796 seconds (real time) Cime Exit Status: 0