- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(0) -> 1 [2] f(s(x)) -> g(x,s(x)) [3] g(0,y) -> y [4] g(s(x),y) -> g(x,+(y,s(x))) [5] +(x,0) -> x [6] +(x,s(y)) -> s(+(x,y)) [7] g(s(x),y) -> g(x,s(+(y,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) >= 1 ; f(s(x)) >= g(x,s(x)) ; g(0,y) >= y ; g(s(x),y) >= g(x,s(+(y,x))) ; g(s(x),y) >= g(x,+(y,s(x))) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; Marked_g(s(x),y) >= Marked_g(x,s(+(y,x))) ; Marked_g(s(x),y) >= Marked_g(x,+(y,s(x))) ; } + Disjunctions:{ { Marked_g(s(x),y) > Marked_g(x,s(+(y,x))) ; } { Marked_g(s(x),y) > Marked_g(x,+(y,s(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) >= 1 constraint: f(s(x)) >= g(x,s(x)) constraint: g(0,y) >= y constraint: g(s(x),y) >= g(x,s(+(y,x))) constraint: g(s(x),y) >= g(x,+(y,s(x))) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: Marked_g(s(x),y) >= Marked_g(x,s(+(y,x))) constraint: Marked_g(s(x),y) >= Marked_g(x,+(y,s(x))) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(0) >= 1 ; f(s(x)) >= g(x,s(x)) ; g(0,y) >= y ; g(s(x),y) >= g(x,s(+(y,x))) ; g(s(x),y) >= g(x,+(y,s(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: f(0) >= 1 constraint: f(s(x)) >= g(x,s(x)) constraint: g(0,y) >= y constraint: g(s(x),y) >= g(x,s(+(y,x))) constraint: g(s(x),y) >= g(x,+(y,s(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] f(0) -> 1 [2] f(s(x)) -> g(x,s(x)) [3] g(0,y) -> y [4] g(s(x),y) -> g(x,+(y,s(x))) [5] +(x,0) -> x [6] +(x,s(y)) -> s(+(x,y)) [7] g(s(x),y) -> g(x,s(+(y,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.): { 1 < f ; f > 1 ; f > g ; f > s ; f > + ; g < f ; g > s ; g > + ; s < f ; s < g ; s < + ; s < Marked_g ; + < f ; + < g ; + > s ; + < Marked_g ; Marked_g > s ; Marked_g > + ; } ]} { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { 1 < f ; f > 1 ; f > g ; f > s ; f > + ; g < f ; g > s ; g > + ; s < f ; s < g ; s < + ; + < f ; + < g ; + > s ; } ]} ]} ]} Cime worked for 0.063020 seconds (real time) Cime Exit Status: 0