- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] primes -> sieve(from(s(s(0)))) [2] from(X) -> cons(X,from(s(X))) [3] head(cons(X,Y)) -> X [4] tail(cons(X,Y)) -> Y [5] if(true,X,Y) -> X [6] if(false,X,Y) -> Y [7] filter(s(s(X)),cons(Y,Z)) -> if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))) [8] sieve(cons(X,Y)) -> cons(X,filter(X,sieve(Y))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { sieve(cons(X,Y)) >= cons(X,filter(X,sieve(Y))) ; from(X) >= cons(X,from(s(X))) ; primes >= sieve(from(s(s(0)))) ; head(cons(X,Y)) >= X ; tail(cons(X,Y)) >= Y ; if(true,X,Y) >= X ; if(false,X,Y) >= Y ; filter(s(s(X)),cons(Y,Z)) >= if(divides(s(s(X)),Y),filter(s(s(X)),Z), cons(Y,filter(X,sieve(Y)))) ; 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: { sieve(cons(X,Y)) >= cons(X,filter(X,sieve(Y))) ; from(X) >= cons(X,from(s(X))) ; primes >= sieve(from(s(s(0)))) ; head(cons(X,Y)) >= X ; tail(cons(X,Y)) >= Y ; if(true,X,Y) >= X ; if(false,X,Y) >= Y ; filter(s(s(X)),cons(Y,Z)) >= if(divides(s(s(X)),Y),filter(s(s(X)),Z), cons(Y,filter(X,sieve(Y)))) ; Marked_from(X) > Marked_from(s(X)) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { sieve(cons(X,Y)) >= cons(X,filter(X,sieve(Y))) ; from(X) >= cons(X,from(s(X))) ; primes >= sieve(from(s(s(0)))) ; head(cons(X,Y)) >= X ; tail(cons(X,Y)) >= Y ; if(true,X,Y) >= X ; if(false,X,Y) >= Y ; filter(s(s(X)),cons(Y,Z)) >= if(divides(s(s(X)),Y),filter(s(s(X)),Z), cons(Y,filter(X,sieve(Y)))) ; 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.(82 bt (120) [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 8.023360 seconds (real time) Cime Exit Status: 0