- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] check(0) -> zero [2] check(s(0)) -> odd [3] check(s(s(0))) -> even [4] check(s(s(s(x)))) -> check(s(x)) [5] half(0) -> 0 [6] half(s(0)) -> 0 [7] half(s(s(x))) -> s(half(x)) [8] plus(0,y) -> y [9] plus(s(x),y) -> s(plus(x,y)) [10] times(x,y) -> timesIter(x,y,0) [11] timesIter(x,y,z) -> if(check(x),x,y,z,plus(z,y)) [12] p(s(x)) -> x [13] p(0) -> 0 [14] if(zero,x,y,z,u) -> z [15] if(odd,x,y,z,u) -> timesIter(p(x),y,u) [16] if(even,x,y,z,u) -> plus(timesIter(half(x),y,half(z)),timesIter(half(x),y,half(s(z)))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 4 components: { --> --> --> --> --> --> } { --> } { --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { check(0) >= zero ; check(s(0)) >= odd ; check(s(s(0))) >= even ; check(s(s(s(x)))) >= check(s(x)) ; half(0) >= 0 ; half(s(0)) >= 0 ; half(s(s(x))) >= s(half(x)) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(x,y)) ; timesIter(x,y,z) >= if(check(x),x,y,z,plus(z,y)) ; times(x,y) >= timesIter(x,y,0) ; if(zero,x,y,z,u) >= z ; if(odd,x,y,z,u) >= timesIter(p(x),y,u) ; if(even,x,y,z,u) >= plus(timesIter(half(x),y,half(z)), timesIter(half(x),y,half(s(z)))) ; p(0) >= 0 ; p(s(x)) >= x ; Marked_if(odd,x,y,z,u) >= Marked_timesIter(p(x),y,u) ; Marked_if(even,x,y,z,u) >= Marked_timesIter(half(x),y,half(s(z))) ; Marked_if(even,x,y,z,u) >= Marked_timesIter(half(x),y,half(z)) ; Marked_timesIter(x,y,z) >= Marked_if(check(x),x,y,z,plus(z,y)) ; } + Disjunctions:{ { Marked_if(odd,x,y,z,u) > Marked_timesIter(p(x),y,u) ; } { Marked_if(even,x,y,z,u) > Marked_timesIter(half(x),y,half(s(z))) ; } { Marked_if(even,x,y,z,u) > Marked_timesIter(half(x),y,half(z)) ; } { Marked_timesIter(x,y,z) > Marked_if(check(x),x,y,z,plus(z,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 === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. === TIMER virtual : 50.000000 === trying sub matrices of size: 1 Matrix interpretation constraints generated. Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. Termination constraints generated. Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 50.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. No solution found for these constraints. APPLY CRITERIA (Simple graph) Found the following constraints: { check(0) >= zero ; check(s(0)) >= odd ; check(s(s(0))) >= even ; check(s(s(s(x)))) >= check(s(x)) ; half(0) >= 0 ; half(s(0)) >= 0 ; half(s(s(x))) >= s(half(x)) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(x,y)) ; timesIter(x,y,z) >= if(check(x),x,y,z,plus(z,y)) ; times(x,y) >= timesIter(x,y,0) ; if(zero,x,y,z,u) >= z ; if(odd,x,y,z,u) >= timesIter(p(x),y,u) ; if(even,x,y,z,u) >= plus(timesIter(half(x),y,half(z)), timesIter(half(x),y,half(s(z)))) ; p(0) >= 0 ; p(s(x)) >= x ; Marked_if(odd,x,y,z,u) > Marked_timesIter(p(x),y,u) ; Marked_if(even,x,y,z,u) >= Marked_timesIter(half(x),y,half(s(z))) ; Marked_if(even,x,y,z,u) > Marked_timesIter(half(x),y,half(z)) ; Marked_timesIter(x,y,z) > Marked_if(check(x),x,y,z,plus(z,y)) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { check(0) >= zero ; check(s(0)) >= odd ; check(s(s(0))) >= even ; check(s(s(s(x)))) >= check(s(x)) ; half(0) >= 0 ; half(s(0)) >= 0 ; half(s(s(x))) >= s(half(x)) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(x,y)) ; timesIter(x,y,z) >= if(check(x),x,y,z,plus(z,y)) ; times(x,y) >= timesIter(x,y,0) ; if(zero,x,y,z,u) >= z ; if(odd,x,y,z,u) >= timesIter(p(x),y,u) ; if(even,x,y,z,u) >= plus(timesIter(half(x),y,half(z)), timesIter(half(x),y,half(s(z)))) ; p(0) >= 0 ; p(s(x)) >= x ; Marked_if(odd,x,y,z,u) > Marked_timesIter(p(x),y,u) ; Marked_if(even,x,y,z,u) >= Marked_timesIter(half(x),y,half(s(z))) ; Marked_if(even,x,y,z,u) > Marked_timesIter(half(x),y,half(z)) ; Marked_timesIter(x,y,z) > Marked_if(check(x),x,y,z,plus(z,y)) ; } + Disjunctions:{ } === 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 === No solution found for these parameters.(66608 bt (67788) [4984]) === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. === TIMER virtual : 50.000000 === trying sub matrices of size: 1 Matrix interpretation constraints generated. Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. Termination constraints generated. Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 50.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. No solution found for these constraints. APPLY CRITERIA (ID_CRIT) NOT SOLVED No proof found Cime worked for 17.279973 seconds (real time) Cime Exit Status: 0