- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] plus(0,x) -> x [2] plus(s(x),y) -> s(plus(p(s(x)),y)) [3] times(0,y) -> 0 [4] times(s(x),y) -> plus(y,times(p(s(x)),y)) [5] exp(x,0) -> s(0) [6] exp(x,s(y)) -> times(x,exp(x,y)) [7] p(s(0)) -> 0 [8] p(s(s(x))) -> s(p(s(x))) [9] tower(x,y) -> towerIter(x,y,s(0)) [10] towerIter(0,y,z) -> z [11] towerIter(s(x),y,z) -> towerIter(p(s(x)),y,exp(y,z)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 5 components: { --> } { --> } { --> } { --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { plus(0,x) >= x ; plus(s(x),y) >= s(plus(p(s(x)),y)) ; p(s(0)) >= 0 ; p(s(s(x))) >= s(p(s(x))) ; times(0,y) >= 0 ; times(s(x),y) >= plus(y,times(p(s(x)),y)) ; exp(x,0) >= s(0) ; exp(x,s(y)) >= times(x,exp(x,y)) ; towerIter(0,y,z) >= z ; towerIter(s(x),y,z) >= towerIter(p(s(x)),y,exp(y,z)) ; tower(x,y) >= towerIter(x,y,s(0)) ; Marked_towerIter(s(x),y,z) >= Marked_towerIter(p(s(x)),y,exp(y,z)) ; } + Disjunctions:{ { Marked_towerIter(s(x),y,z) > Marked_towerIter(p(s(x)),y,exp(y,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 === === 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: { plus(0,x) >= x ; plus(s(x),y) >= s(plus(p(s(x)),y)) ; p(s(0)) >= 0 ; p(s(s(x))) >= s(p(s(x))) ; times(0,y) >= 0 ; times(s(x),y) >= plus(y,times(p(s(x)),y)) ; exp(x,0) >= s(0) ; exp(x,s(y)) >= times(x,exp(x,y)) ; towerIter(0,y,z) >= z ; towerIter(s(x),y,z) >= towerIter(p(s(x)),y,exp(y,z)) ; tower(x,y) >= towerIter(x,y,s(0)) ; Marked_towerIter(s(x),y,z) > Marked_towerIter(p(s(x)),y,exp(y,z)) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { plus(0,x) >= x ; plus(s(x),y) >= s(plus(p(s(x)),y)) ; p(s(0)) >= 0 ; p(s(s(x))) >= s(p(s(x))) ; times(0,y) >= 0 ; times(s(x),y) >= plus(y,times(p(s(x)),y)) ; exp(x,0) >= s(0) ; exp(x,s(y)) >= times(x,exp(x,y)) ; towerIter(0,y,z) >= z ; towerIter(s(x),y,z) >= towerIter(p(s(x)),y,exp(y,z)) ; tower(x,y) >= towerIter(x,y,s(0)) ; Marked_towerIter(s(x),y,z) > Marked_towerIter(p(s(x)),y,exp(y,z)) ; } + 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.(896 bt (805) [306]) === 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 2.954510 seconds (real time) Cime Exit Status: 0