- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] fac(0) -> 1 [2] fac(s(x)) -> *(s(x),fac(x)) [3] floop(0,y) -> y [4] floop(s(x),y) -> floop(x, *(s(x),y)) [5] *(x,0) -> 0 [6] *(x,s(y)) -> +( *(x,y),x) [7] +(x,0) -> x [8] +(x,s(y)) -> s(+(x,y)) [9] 1 -> s(0) [10] fac(0) -> s(0) 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: { 1 >= s(0) ; fac(0) >= 1 ; fac(0) >= s(0) ; fac(s(x)) >= *(s(x),fac(x)) ; *(x,0) >= 0 ; *(x,s(y)) >= +( *(x,y),x) ; floop(0,y) >= y ; floop(s(x),y) >= floop(x, *(s(x),y)) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; Marked_fac(s(x)) >= Marked_fac(x) ; } + Disjunctions:{ { Marked_fac(s(x)) > Marked_fac(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: 1 >= s(0) constraint: fac(0) >= 1 constraint: fac(0) >= s(0) constraint: fac(s(x)) >= *(s(x),fac(x)) constraint: *(x,0) >= 0 constraint: *(x,s(y)) >= +( *(x,y),x) constraint: floop(0,y) >= y constraint: floop(s(x),y) >= floop(x, *(s(x),y)) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: Marked_fac(s(x)) >= Marked_fac(x) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { 1 >= s(0) ; fac(0) >= 1 ; fac(0) >= s(0) ; fac(s(x)) >= *(s(x),fac(x)) ; *(x,0) >= 0 ; *(x,s(y)) >= +( *(x,y),x) ; floop(0,y) >= y ; floop(s(x),y) >= floop(x, *(s(x),y)) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; Marked_floop(s(x),y) >= Marked_floop(x, *(s(x),y)) ; } + Disjunctions:{ { Marked_floop(s(x),y) > Marked_floop(x, *(s(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: 1 >= s(0) constraint: fac(0) >= 1 constraint: fac(0) >= s(0) constraint: fac(s(x)) >= *(s(x),fac(x)) constraint: *(x,0) >= 0 constraint: *(x,s(y)) >= +( *(x,y),x) constraint: floop(0,y) >= y constraint: floop(s(x),y) >= floop(x, *(s(x),y)) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: Marked_floop(s(x),y) >= Marked_floop(x, *(s(x),y)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { 1 >= s(0) ; fac(0) >= 1 ; fac(0) >= s(0) ; fac(s(x)) >= *(s(x),fac(x)) ; *(x,0) >= 0 ; *(x,s(y)) >= +( *(x,y),x) ; floop(0,y) >= y ; floop(s(x),y) >= floop(x, *(s(x),y)) ; +(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: 1 >= s(0) constraint: fac(0) >= 1 constraint: fac(0) >= s(0) constraint: fac(s(x)) >= *(s(x),fac(x)) constraint: *(x,0) >= 0 constraint: *(x,s(y)) >= +( *(x,y),x) constraint: floop(0,y) >= y constraint: floop(s(x),y) >= floop(x, *(s(x),y)) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: Marked_*(x,s(y)) >= Marked_*(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { 1 >= s(0) ; fac(0) >= 1 ; fac(0) >= s(0) ; fac(s(x)) >= *(s(x),fac(x)) ; *(x,0) >= 0 ; *(x,s(y)) >= +( *(x,y),x) ; floop(0,y) >= y ; floop(s(x),y) >= floop(x, *(s(x),y)) ; +(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: 1 >= s(0) constraint: fac(0) >= 1 constraint: fac(0) >= s(0) constraint: fac(s(x)) >= *(s(x),fac(x)) constraint: *(x,0) >= 0 constraint: *(x,s(y)) >= +( *(x,y),x) constraint: floop(0,y) >= y constraint: floop(s(x),y) >= floop(x, *(s(x),y)) 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: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] fac(0) -> 1 [2] fac(s(x)) -> *(s(x),fac(x)) [3] floop(0,y) -> y [4] floop(s(x),y) -> floop(x, *(s(x),y)) [5] *(x,0) -> 0 [6] *(x,s(y)) -> +( *(x,y),x) [7] +(x,0) -> x [8] +(x,s(y)) -> s(+(x,y)) [9] 1 -> s(0) [10] fac(0) -> s(0) , 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 < fac ; 1 > 0 ; 1 > s ; fac > 1 ; fac > 0 ; fac > * ; fac > s ; fac > + ; 0 < 1 ; 0 < fac ; * < fac ; * > s ; * < floop ; * > + ; s < 1 ; s < fac ; s < * ; s < floop ; s < + ; floop > * ; floop > s ; floop > + ; + < fac ; + < * ; + > s ; + < floop ; } ]} { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { 1 < fac ; 1 > 0 ; 1 > s ; fac > 1 ; fac > 0 ; fac > * ; fac > s ; fac > + ; 0 < 1 ; 0 < fac ; * < fac ; * > s ; * < floop ; * > + ; * < Marked_floop ; s < 1 ; s < fac ; s < * ; s < floop ; s < + ; s < Marked_floop ; floop > * ; floop > s ; floop > + ; + < fac ; + < * ; + > s ; + < floop ; + < Marked_floop ; Marked_floop > * ; Marked_floop > s ; Marked_floop > + ; } ]} { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { 1 < fac ; 1 > 0 ; 1 > s ; fac > 1 ; fac > 0 ; fac > * ; fac > s ; fac > + ; 0 < 1 ; 0 < fac ; * < fac ; * > s ; * < floop ; * > + ; s < 1 ; s < fac ; s < * ; s < floop ; s < + ; floop > * ; floop > s ; floop > + ; + < fac ; + < * ; + > s ; + < floop ; } ]} { DP termination of: , CRITERION: ORD [ Solution found: RPO with AFS = AFS: and precedence: prec (All symbols are Lex.): { 1 < fac ; 1 > 0 ; 1 > s ; fac > 1 ; fac > 0 ; fac > * ; fac > s ; fac > + ; 0 < 1 ; 0 < fac ; * < fac ; * > s ; * < floop ; * > + ; s < 1 ; s < fac ; s < * ; s < floop ; s < + ; floop > * ; floop > s ; floop > + ; + < fac ; + < * ; + > s ; + < floop ; } ]} ]} ]} Cime worked for 0.130001 seconds (real time) Cime Exit Status: 0