- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] from(X) -> cons(X,from(s(X))) [2] 2ndspos(0,Z) -> rnil [3] 2ndspos(s(N),cons(X,Z)) -> 2ndspos(s(N),cons2(X,Z)) [4] 2ndspos(s(N),cons2(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,Z)) [5] 2ndsneg(0,Z) -> rnil [6] 2ndsneg(s(N),cons(X,Z)) -> 2ndsneg(s(N),cons2(X,Z)) [7] 2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z)) [8] pi(X) -> 2ndspos(X,from(0)) [9] plus(0,Y) -> Y [10] plus(s(X),Y) -> s(plus(X,Y)) [11] times(0,Y) -> 0 [12] times(s(X),Y) -> plus(Y,times(X,Y)) [13] square(X) -> times(X,X) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 4 components: { --> --> --> --> --> --> } { --> } { --> } { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_2ndsneg -> 1 Marked_2ndspos -> 1 APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { from(X) >= cons(X,from(s(X))) ; 2ndspos(s(N),cons(X,Z)) >= 2ndspos(s(N),cons2(X,Z)) ; 2ndspos(s(N),cons2(X,cons(Y,Z))) >= rcons(posrecip(Y),2ndsneg(N,Z)) ; 2ndspos(0,Z) >= rnil ; 2ndsneg(s(N),cons(X,Z)) >= 2ndsneg(s(N),cons2(X,Z)) ; 2ndsneg(s(N),cons2(X,cons(Y,Z))) >= rcons(negrecip(Y),2ndspos(N,Z)) ; 2ndsneg(0,Z) >= rnil ; pi(X) >= 2ndspos(X,from(0)) ; plus(s(X),Y) >= s(plus(X,Y)) ; plus(0,Y) >= Y ; times(s(X),Y) >= plus(Y,times(X,Y)) ; times(0,Y) >= 0 ; square(X) >= times(X,X) ; Marked_from(X) >= Marked_from(s(X)) ; } + Disjunctions:{ { Marked_from(X) > Marked_from(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 === === 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: { from(X) >= cons(X,from(s(X))) ; 2ndspos(s(N),cons(X,Z)) >= 2ndspos(s(N),cons2(X,Z)) ; 2ndspos(s(N),cons2(X,cons(Y,Z))) >= rcons(posrecip(Y),2ndsneg(N,Z)) ; 2ndspos(0,Z) >= rnil ; 2ndsneg(s(N),cons(X,Z)) >= 2ndsneg(s(N),cons2(X,Z)) ; 2ndsneg(s(N),cons2(X,cons(Y,Z))) >= rcons(negrecip(Y),2ndspos(N,Z)) ; 2ndsneg(0,Z) >= rnil ; pi(X) >= 2ndspos(X,from(0)) ; plus(s(X),Y) >= s(plus(X,Y)) ; plus(0,Y) >= Y ; times(s(X),Y) >= plus(Y,times(X,Y)) ; times(0,Y) >= 0 ; square(X) >= times(X,X) ; Marked_from(X) > Marked_from(s(X)) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { from(X) >= cons(X,from(s(X))) ; 2ndspos(s(N),cons(X,Z)) >= 2ndspos(s(N),cons2(X,Z)) ; 2ndspos(s(N),cons2(X,cons(Y,Z))) >= rcons(posrecip(Y),2ndsneg(N,Z)) ; 2ndspos(0,Z) >= rnil ; 2ndsneg(s(N),cons(X,Z)) >= 2ndsneg(s(N),cons2(X,Z)) ; 2ndsneg(s(N),cons2(X,cons(Y,Z))) >= rcons(negrecip(Y),2ndspos(N,Z)) ; 2ndsneg(0,Z) >= rnil ; pi(X) >= 2ndspos(X,from(0)) ; plus(s(X),Y) >= s(plus(X,Y)) ; plus(0,Y) >= Y ; times(s(X),Y) >= plus(Y,times(X,Y)) ; times(0,Y) >= 0 ; square(X) >= times(X,X) ; Marked_from(X) > Marked_from(s(X)) ; } + Disjunctions:{ } === TIMER virtual : 10.000000 === Entering poly_solver === 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.(118 bt (180) [9]) === TIMER virtual : 15.000000 === Entering poly_solver === 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 === 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 0.727923 seconds (real time) Cime Exit Status: 0