- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__primes -> a__sieve(a__from(s(s(0)))) [2] a__from(X) -> cons(mark(X),from(s(X))) [3] a__head(cons(X,Y)) -> mark(X) [4] a__tail(cons(X,Y)) -> mark(Y) [5] a__if(true,X,Y) -> mark(X) [6] a__if(false,X,Y) -> mark(Y) [7] a__filter(s(s(X)),cons(Y,Z)) -> a__if(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z), cons(Y,filter(X,sieve(Y)))) [8] a__sieve(cons(X,Y)) -> cons(mark(X),filter(X,sieve(Y))) [9] mark(primes) -> a__primes [10] mark(sieve(X)) -> a__sieve(mark(X)) [11] mark(from(X)) -> a__from(mark(X)) [12] mark(head(X)) -> a__head(mark(X)) [13] mark(tail(X)) -> a__tail(mark(X)) [14] mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3) [15] mark(filter(X1,X2)) -> a__filter(mark(X1),mark(X2)) [16] mark(s(X)) -> s(mark(X)) [17] mark(0) -> 0 [18] mark(cons(X1,X2)) -> cons(mark(X1),X2) [19] mark(true) -> true [20] mark(false) -> false [21] mark(divides(X1,X2)) -> divides(mark(X1),mark(X2)) [22] a__primes -> primes [23] a__sieve(X) -> sieve(X) [24] a__from(X) -> from(X) [25] a__head(X) -> head(X) [26] a__tail(X) -> tail(X) [27] a__if(X1,X2,X3) -> if(X1,X2,X3) [28] a__filter(X1,X2) -> filter(X1,X2) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { a__sieve(cons(X,Y)) >= cons(mark(X),filter(X,sieve(Y))) ; a__sieve(X) >= sieve(X) ; a__from(X) >= cons(mark(X),from(s(X))) ; a__from(X) >= from(X) ; a__primes >= a__sieve(a__from(s(s(0)))) ; a__primes >= primes ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(from(X)) >= a__from(mark(X)) ; mark(true) >= true ; mark(false) >= false ; mark(divides(X1,X2)) >= divides(mark(X1),mark(X2)) ; mark(filter(X1,X2)) >= a__filter(mark(X1),mark(X2)) ; mark(sieve(X)) >= a__sieve(mark(X)) ; mark(primes) >= a__primes ; mark(head(X)) >= a__head(mark(X)) ; mark(tail(X)) >= a__tail(mark(X)) ; mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3) ; a__head(cons(X,Y)) >= mark(X) ; a__head(X) >= head(X) ; a__tail(cons(X,Y)) >= mark(Y) ; a__tail(X) >= tail(X) ; a__if(true,X,Y) >= mark(X) ; a__if(false,X,Y) >= mark(Y) ; a__if(X1,X2,X3) >= if(X1,X2,X3) ; a__filter(s(s(X)),cons(Y,Z)) >= a__if(divides(s(s(mark(X))),mark(Y)), filter(s(s(X)),Z), cons(Y,filter(X,sieve(Y)))) ; a__filter(X1,X2) >= filter(X1,X2) ; Marked_a__filter(s(s(X)),cons(Y,Z)) >= Marked_mark(X) ; Marked_a__filter(s(s(X)),cons(Y,Z)) >= Marked_mark(Y) ; Marked_a__if(true,X,Y) >= Marked_mark(X) ; Marked_a__if(false,X,Y) >= Marked_mark(Y) ; Marked_a__tail(cons(X,Y)) >= Marked_mark(Y) ; Marked_a__head(cons(X,Y)) >= Marked_mark(X) ; Marked_a__from(X) >= Marked_mark(X) ; Marked_a__sieve(cons(X,Y)) >= Marked_mark(X) ; Marked_a__primes >= Marked_a__from(s(s(0))) ; Marked_a__primes >= Marked_a__sieve(a__from(s(s(0)))) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(from(X)) >= Marked_a__from(mark(X)) ; Marked_mark(from(X)) >= Marked_mark(X) ; Marked_mark(divides(X1,X2)) >= Marked_mark(X1) ; Marked_mark(divides(X1,X2)) >= Marked_mark(X2) ; Marked_mark(filter(X1,X2)) >= Marked_a__filter(mark(X1),mark(X2)) ; Marked_mark(filter(X1,X2)) >= Marked_mark(X1) ; Marked_mark(filter(X1,X2)) >= Marked_mark(X2) ; Marked_mark(sieve(X)) >= Marked_a__sieve(mark(X)) ; Marked_mark(sieve(X)) >= Marked_mark(X) ; Marked_mark(primes) >= Marked_a__primes ; Marked_mark(head(X)) >= Marked_a__head(mark(X)) ; Marked_mark(head(X)) >= Marked_mark(X) ; Marked_mark(tail(X)) >= Marked_a__tail(mark(X)) ; Marked_mark(tail(X)) >= Marked_mark(X) ; Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),X2,X3) ; Marked_mark(if(X1,X2,X3)) >= Marked_mark(X1) ; } + Disjunctions:{ { Marked_a__filter(s(s(X)),cons(Y,Z)) > Marked_mark(X) ; } { Marked_a__filter(s(s(X)),cons(Y,Z)) > Marked_mark(Y) ; } { Marked_a__if(true,X,Y) > Marked_mark(X) ; } { Marked_a__if(false,X,Y) > Marked_mark(Y) ; } { Marked_a__tail(cons(X,Y)) > Marked_mark(Y) ; } { Marked_a__head(cons(X,Y)) > Marked_mark(X) ; } { Marked_a__from(X) > Marked_mark(X) ; } { Marked_a__sieve(cons(X,Y)) > Marked_mark(X) ; } { Marked_a__primes > Marked_a__from(s(s(0))) ; } { Marked_a__primes > Marked_a__sieve(a__from(s(s(0)))) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(from(X)) > Marked_a__from(mark(X)) ; } { Marked_mark(from(X)) > Marked_mark(X) ; } { Marked_mark(divides(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(divides(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(filter(X1,X2)) > Marked_a__filter(mark(X1),mark(X2)) ; } { Marked_mark(filter(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(filter(X1,X2)) > Marked_mark(X2) ; } { Marked_mark(sieve(X)) > Marked_a__sieve(mark(X)) ; } { Marked_mark(sieve(X)) > Marked_mark(X) ; } { Marked_mark(primes) > Marked_a__primes ; } { Marked_mark(head(X)) > Marked_a__head(mark(X)) ; } { Marked_mark(head(X)) > Marked_mark(X) ; } { Marked_mark(tail(X)) > Marked_a__tail(mark(X)) ; } { Marked_mark(tail(X)) > Marked_mark(X) ; } { Marked_mark(if(X1,X2,X3)) > Marked_a__if(mark(X1),X2,X3) ; } { Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ; } } === 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 === Time out for these parameters. === 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 timeout reached === STOPING TIMER virtual === Time out 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: { a__sieve(cons(X,Y)) >= cons(mark(X),filter(X,sieve(Y))) ; a__sieve(X) >= sieve(X) ; a__from(X) >= cons(mark(X),from(s(X))) ; a__from(X) >= from(X) ; a__primes >= a__sieve(a__from(s(s(0)))) ; a__primes >= primes ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(from(X)) >= a__from(mark(X)) ; mark(true) >= true ; mark(false) >= false ; mark(divides(X1,X2)) >= divides(mark(X1),mark(X2)) ; mark(filter(X1,X2)) >= a__filter(mark(X1),mark(X2)) ; mark(sieve(X)) >= a__sieve(mark(X)) ; mark(primes) >= a__primes ; mark(head(X)) >= a__head(mark(X)) ; mark(tail(X)) >= a__tail(mark(X)) ; mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3) ; a__head(cons(X,Y)) >= mark(X) ; a__head(X) >= head(X) ; a__tail(cons(X,Y)) >= mark(Y) ; a__tail(X) >= tail(X) ; a__if(true,X,Y) >= mark(X) ; a__if(false,X,Y) >= mark(Y) ; a__if(X1,X2,X3) >= if(X1,X2,X3) ; a__filter(s(s(X)),cons(Y,Z)) >= a__if(divides(s(s(mark(X))),mark(Y)), filter(s(s(X)),Z), cons(Y,filter(X,sieve(Y)))) ; a__filter(X1,X2) >= filter(X1,X2) ; Marked_a__filter(s(s(X)),cons(Y,Z)) > Marked_mark(X) ; Marked_a__filter(s(s(X)),cons(Y,Z)) > Marked_mark(Y) ; Marked_a__if(true,X,Y) > Marked_mark(X) ; Marked_a__if(false,X,Y) > Marked_mark(Y) ; Marked_a__tail(cons(X,Y)) > Marked_mark(Y) ; Marked_a__head(cons(X,Y)) > Marked_mark(X) ; Marked_a__from(X) > Marked_mark(X) ; Marked_a__sieve(cons(X,Y)) > Marked_mark(X) ; Marked_a__primes > Marked_a__from(s(s(0))) ; Marked_a__primes > Marked_a__sieve(a__from(s(s(0)))) ; Marked_mark(s(X)) > Marked_mark(X) ; Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; Marked_mark(from(X)) >= Marked_a__from(mark(X)) ; Marked_mark(from(X)) > Marked_mark(X) ; Marked_mark(divides(X1,X2)) > Marked_mark(X1) ; Marked_mark(divides(X1,X2)) > Marked_mark(X2) ; Marked_mark(filter(X1,X2)) >= Marked_a__filter(mark(X1),mark(X2)) ; Marked_mark(filter(X1,X2)) > Marked_mark(X1) ; Marked_mark(filter(X1,X2)) > Marked_mark(X2) ; Marked_mark(sieve(X)) >= Marked_a__sieve(mark(X)) ; Marked_mark(sieve(X)) > Marked_mark(X) ; Marked_mark(primes) >= Marked_a__primes ; Marked_mark(head(X)) >= Marked_a__head(mark(X)) ; Marked_mark(head(X)) > Marked_mark(X) ; Marked_mark(tail(X)) >= Marked_a__tail(mark(X)) ; Marked_mark(tail(X)) > Marked_mark(X) ; Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),X2,X3) ; Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { a__sieve(cons(X,Y)) >= cons(mark(X),filter(X,sieve(Y))) ; a__sieve(X) >= sieve(X) ; a__from(X) >= cons(mark(X),from(s(X))) ; a__from(X) >= from(X) ; a__primes >= a__sieve(a__from(s(s(0)))) ; a__primes >= primes ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(from(X)) >= a__from(mark(X)) ; mark(true) >= true ; mark(false) >= false ; mark(divides(X1,X2)) >= divides(mark(X1),mark(X2)) ; mark(filter(X1,X2)) >= a__filter(mark(X1),mark(X2)) ; mark(sieve(X)) >= a__sieve(mark(X)) ; mark(primes) >= a__primes ; mark(head(X)) >= a__head(mark(X)) ; mark(tail(X)) >= a__tail(mark(X)) ; mark(if(X1,X2,X3)) >= a__if(mark(X1),X2,X3) ; a__head(cons(X,Y)) >= mark(X) ; a__head(X) >= head(X) ; a__tail(cons(X,Y)) >= mark(Y) ; a__tail(X) >= tail(X) ; a__if(true,X,Y) >= mark(X) ; a__if(false,X,Y) >= mark(Y) ; a__if(X1,X2,X3) >= if(X1,X2,X3) ; a__filter(s(s(X)),cons(Y,Z)) >= a__if(divides(s(s(mark(X))),mark(Y)), filter(s(s(X)),Z), cons(Y,filter(X,sieve(Y)))) ; a__filter(X1,X2) >= filter(X1,X2) ; Marked_a__filter(s(s(X)),cons(Y,Z)) > Marked_mark(X) ; Marked_a__filter(s(s(X)),cons(Y,Z)) > Marked_mark(Y) ; Marked_a__if(true,X,Y) > Marked_mark(X) ; Marked_a__if(false,X,Y) > Marked_mark(Y) ; Marked_a__tail(cons(X,Y)) > Marked_mark(Y) ; Marked_a__head(cons(X,Y)) > Marked_mark(X) ; Marked_a__from(X) > Marked_mark(X) ; Marked_a__sieve(cons(X,Y)) > Marked_mark(X) ; Marked_a__primes > Marked_a__from(s(s(0))) ; Marked_a__primes > Marked_a__sieve(a__from(s(s(0)))) ; Marked_mark(s(X)) > Marked_mark(X) ; Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; Marked_mark(from(X)) >= Marked_a__from(mark(X)) ; Marked_mark(from(X)) > Marked_mark(X) ; Marked_mark(divides(X1,X2)) > Marked_mark(X1) ; Marked_mark(divides(X1,X2)) > Marked_mark(X2) ; Marked_mark(filter(X1,X2)) >= Marked_a__filter(mark(X1),mark(X2)) ; Marked_mark(filter(X1,X2)) > Marked_mark(X1) ; Marked_mark(filter(X1,X2)) > Marked_mark(X2) ; Marked_mark(sieve(X)) >= Marked_a__sieve(mark(X)) ; Marked_mark(sieve(X)) > Marked_mark(X) ; Marked_mark(primes) >= Marked_a__primes ; Marked_mark(head(X)) >= Marked_a__head(mark(X)) ; Marked_mark(head(X)) > Marked_mark(X) ; Marked_mark(tail(X)) >= Marked_a__tail(mark(X)) ; Marked_mark(tail(X)) > Marked_mark(X) ; Marked_mark(if(X1,X2,X3)) >= Marked_a__if(mark(X1),X2,X3) ; Marked_mark(if(X1,X2,X3)) > Marked_mark(X1) ; } + 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.(8758 bt (9543) [3666]) === 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 timeout reached === STOPING TIMER virtual === Time out 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 132.339431 seconds (real time) Cime Exit Status: 0