- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] f(x,0,0) -> s(x) [2] f(0,y,0) -> s(y) [3] f(0,0,z) -> s(z) [4] f(s(0),y,z) -> f(0,s(y),s(z)) [5] f(s(x),s(y),0) -> f(x,y,s(0)) [6] f(s(x),0,s(z)) -> f(x,s(0),z) [7] f(0,s(0),s(0)) -> s(s(0)) [8] f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z)) [9] f(0,s(s(y)),s(0)) -> f(0,y,s(0)) [10] f(0,s(0),s(s(z))) -> f(0,s(0),z) [11] f(0,s(s(y)),s(s(z))) -> f(0,y,f(0,s(s(y)),s(z))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 4 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> } { --> } { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(s(0),y,z) >= f(0,s(y),s(z)) ; f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z)) ; f(s(x),s(y),0) >= f(x,y,s(0)) ; f(s(x),0,s(z)) >= f(x,s(0),z) ; f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z))) ; f(0,s(s(y)),s(0)) >= f(0,y,s(0)) ; f(0,s(0),s(s(z))) >= f(0,s(0),z) ; f(0,s(0),s(0)) >= s(s(0)) ; f(0,0,z) >= s(z) ; f(0,y,0) >= s(y) ; f(x,0,0) >= s(x) ; Marked_f(s(x),s(y),s(z)) >= Marked_f(s(x),s(y),z) ; Marked_f(s(x),s(y),s(z)) >= Marked_f(x,y,f(s(x),s(y),z)) ; Marked_f(s(x),s(y),0) >= Marked_f(x,y,s(0)) ; Marked_f(s(x),0,s(z)) >= Marked_f(x,s(0),z) ; } + Disjunctions:{ { Marked_f(s(x),s(y),s(z)) > Marked_f(s(x),s(y),z) ; } { Marked_f(s(x),s(y),s(z)) > Marked_f(x,y,f(s(x),s(y),z)) ; } { Marked_f(s(x),s(y),0) > Marked_f(x,y,s(0)) ; } { Marked_f(s(x),0,s(z)) > Marked_f(x,s(0),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 === 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(s(0),y,z) >= f(0,s(y),s(z)) constraint: f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z)) constraint: f(s(x),s(y),0) >= f(x,y,s(0)) constraint: f(s(x),0,s(z)) >= f(x,s(0),z) constraint: f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z))) constraint: f(0,s(s(y)),s(0)) >= f(0,y,s(0)) constraint: f(0,s(0),s(s(z))) >= f(0,s(0),z) constraint: f(0,s(0),s(0)) >= s(s(0)) constraint: f(0,0,z) >= s(z) constraint: f(0,y,0) >= s(y) constraint: f(x,0,0) >= s(x) constraint: Marked_f(s(x),s(y),s(z)) >= Marked_f(s(x),s(y),z) constraint: Marked_f(s(x),s(y),s(z)) >= Marked_f(x,y,f(s(x),s(y),z)) constraint: Marked_f(s(x),s(y),0) >= Marked_f(x,y,s(0)) constraint: Marked_f(s(x),0,s(z)) >= Marked_f(x,s(0),z) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(s(0),y,z) >= f(0,s(y),s(z)) ; f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z)) ; f(s(x),s(y),0) >= f(x,y,s(0)) ; f(s(x),0,s(z)) >= f(x,s(0),z) ; f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z))) ; f(0,s(s(y)),s(0)) >= f(0,y,s(0)) ; f(0,s(0),s(s(z))) >= f(0,s(0),z) ; f(0,s(0),s(0)) >= s(s(0)) ; f(0,0,z) >= s(z) ; f(0,y,0) >= s(y) ; f(x,0,0) >= s(x) ; Marked_f(0,s(s(y)),s(s(z))) >= Marked_f(0,s(s(y)),s(z)) ; Marked_f(0,s(s(y)),s(s(z))) >= Marked_f(0,y,f(0,s(s(y)),s(z))) ; } + Disjunctions:{ { Marked_f(0,s(s(y)),s(s(z))) > Marked_f(0,s(s(y)),s(z)) ; } { Marked_f(0,s(s(y)),s(s(z))) > Marked_f(0,y,f(0,s(s(y)),s(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 === 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(s(0),y,z) >= f(0,s(y),s(z)) constraint: f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z)) constraint: f(s(x),s(y),0) >= f(x,y,s(0)) constraint: f(s(x),0,s(z)) >= f(x,s(0),z) constraint: f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z))) constraint: f(0,s(s(y)),s(0)) >= f(0,y,s(0)) constraint: f(0,s(0),s(s(z))) >= f(0,s(0),z) constraint: f(0,s(0),s(0)) >= s(s(0)) constraint: f(0,0,z) >= s(z) constraint: f(0,y,0) >= s(y) constraint: f(x,0,0) >= s(x) constraint: Marked_f(0,s(s(y)),s(s(z))) >= Marked_f(0,s(s(y)),s(z)) constraint: Marked_f(0,s(s(y)),s(s(z))) >= Marked_f(0,y,f(0,s(s(y)),s(z))) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(s(0),y,z) >= f(0,s(y),s(z)) ; f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z)) ; f(s(x),s(y),0) >= f(x,y,s(0)) ; f(s(x),0,s(z)) >= f(x,s(0),z) ; f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z))) ; f(0,s(s(y)),s(0)) >= f(0,y,s(0)) ; f(0,s(0),s(s(z))) >= f(0,s(0),z) ; f(0,s(0),s(0)) >= s(s(0)) ; f(0,0,z) >= s(z) ; f(0,y,0) >= s(y) ; f(x,0,0) >= s(x) ; Marked_f(0,s(s(y)),s(0)) >= Marked_f(0,y,s(0)) ; } + Disjunctions:{ { Marked_f(0,s(s(y)),s(0)) > Marked_f(0,y,s(0)) ; } } === 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(s(0),y,z) >= f(0,s(y),s(z)) constraint: f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z)) constraint: f(s(x),s(y),0) >= f(x,y,s(0)) constraint: f(s(x),0,s(z)) >= f(x,s(0),z) constraint: f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z))) constraint: f(0,s(s(y)),s(0)) >= f(0,y,s(0)) constraint: f(0,s(0),s(s(z))) >= f(0,s(0),z) constraint: f(0,s(0),s(0)) >= s(s(0)) constraint: f(0,0,z) >= s(z) constraint: f(0,y,0) >= s(y) constraint: f(x,0,0) >= s(x) constraint: Marked_f(0,s(s(y)),s(0)) >= Marked_f(0,y,s(0)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { f(s(0),y,z) >= f(0,s(y),s(z)) ; f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z)) ; f(s(x),s(y),0) >= f(x,y,s(0)) ; f(s(x),0,s(z)) >= f(x,s(0),z) ; f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z))) ; f(0,s(s(y)),s(0)) >= f(0,y,s(0)) ; f(0,s(0),s(s(z))) >= f(0,s(0),z) ; f(0,s(0),s(0)) >= s(s(0)) ; f(0,0,z) >= s(z) ; f(0,y,0) >= s(y) ; f(x,0,0) >= s(x) ; Marked_f(0,s(0),s(s(z))) >= Marked_f(0,s(0),z) ; } + Disjunctions:{ { Marked_f(0,s(0),s(s(z))) > Marked_f(0,s(0),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 === 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(s(0),y,z) >= f(0,s(y),s(z)) constraint: f(s(x),s(y),s(z)) >= f(x,y,f(s(x),s(y),z)) constraint: f(s(x),s(y),0) >= f(x,y,s(0)) constraint: f(s(x),0,s(z)) >= f(x,s(0),z) constraint: f(0,s(s(y)),s(s(z))) >= f(0,y,f(0,s(s(y)),s(z))) constraint: f(0,s(s(y)),s(0)) >= f(0,y,s(0)) constraint: f(0,s(0),s(s(z))) >= f(0,s(0),z) constraint: f(0,s(0),s(0)) >= s(s(0)) constraint: f(0,0,z) >= s(z) constraint: f(0,y,0) >= s(y) constraint: f(x,0,0) >= s(x) constraint: Marked_f(0,s(0),s(s(z))) >= Marked_f(0,s(0),z) APPLY CRITERIA (Graph splitting) Found 0 components: 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] f(x,0,0) -> s(x) [2] f(0,y,0) -> s(y) [3] f(0,0,z) -> s(z) [4] f(s(0),y,z) -> f(0,s(y),s(z)) [5] f(s(x),s(y),0) -> f(x,y,s(0)) [6] f(s(x),0,s(z)) -> f(x,s(0),z) [7] f(0,s(0),s(0)) -> s(s(0)) [8] f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z)) [9] f(0,s(s(y)),s(0)) -> f(0,y,s(0)) [10] f(0,s(0),s(s(z))) -> f(0,s(0),z) [11] f(0,s(s(y)),s(s(z))) -> f(0,y,f(0,s(s(y)),s(z))) , 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.): { s < f ; s < Marked_f ; f > s ; f < Marked_f ; Marked_f > s ; Marked_f > f ; } ]} { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { s < f ; s < Marked_f ; f > s ; f < Marked_f ; Marked_f > s ; Marked_f > f ; } ]} { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { s < f ; f > s ; } ]} { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { s < f ; f > s ; } ]} ]} ]} Cime worked for 0.309521 seconds (real time) Cime Exit Status: 0