- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] a__f(X) -> cons(mark(X),f(g(X))) [2] a__g(0) -> s(0) [3] a__g(s(X)) -> s(s(a__g(mark(X)))) [4] a__sel(0,cons(X,Y)) -> mark(X) [5] a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z)) [6] mark(f(X)) -> a__f(mark(X)) [7] mark(g(X)) -> a__g(mark(X)) [8] mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2)) [9] mark(cons(X1,X2)) -> cons(mark(X1),X2) [10] mark(0) -> 0 [11] mark(s(X)) -> s(mark(X)) [12] a__f(X) -> f(X) [13] a__g(X) -> g(X) [14] a__sel(X1,X2) -> sel(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: { mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(f(X)) >= a__f(mark(X)) ; mark(g(X)) >= a__g(mark(X)) ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(sel(X1,X2)) >= a__sel(mark(X1),mark(X2)) ; a__f(X) >= cons(mark(X),f(g(X))) ; a__f(X) >= f(X) ; a__g(s(X)) >= s(s(a__g(mark(X)))) ; a__g(0) >= s(0) ; a__g(X) >= g(X) ; a__sel(s(X),cons(Y,Z)) >= a__sel(mark(X),mark(Z)) ; a__sel(0,cons(X,Y)) >= mark(X) ; a__sel(X1,X2) >= sel(X1,X2) ; Marked_a__sel(s(X),cons(Y,Z)) >= Marked_a__sel(mark(X),mark(Z)) ; Marked_a__sel(s(X),cons(Y,Z)) >= Marked_mark(X) ; Marked_a__sel(s(X),cons(Y,Z)) >= Marked_mark(Z) ; Marked_a__sel(0,cons(X,Y)) >= Marked_mark(X) ; Marked_a__g(s(X)) >= Marked_a__g(mark(X)) ; Marked_a__g(s(X)) >= Marked_mark(X) ; Marked_a__f(X) >= Marked_mark(X) ; Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ; Marked_mark(f(X)) >= Marked_a__f(mark(X)) ; Marked_mark(f(X)) >= Marked_mark(X) ; Marked_mark(g(X)) >= Marked_a__g(mark(X)) ; Marked_mark(g(X)) >= Marked_mark(X) ; Marked_mark(s(X)) >= Marked_mark(X) ; Marked_mark(sel(X1,X2)) >= Marked_a__sel(mark(X1),mark(X2)) ; Marked_mark(sel(X1,X2)) >= Marked_mark(X1) ; Marked_mark(sel(X1,X2)) >= Marked_mark(X2) ; } + Disjunctions:{ { Marked_a__sel(s(X),cons(Y,Z)) > Marked_a__sel(mark(X),mark(Z)) ; } { Marked_a__sel(s(X),cons(Y,Z)) > Marked_mark(X) ; } { Marked_a__sel(s(X),cons(Y,Z)) > Marked_mark(Z) ; } { Marked_a__sel(0,cons(X,Y)) > Marked_mark(X) ; } { Marked_a__g(s(X)) > Marked_a__g(mark(X)) ; } { Marked_a__g(s(X)) > Marked_mark(X) ; } { Marked_a__f(X) > Marked_mark(X) ; } { Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(f(X)) > Marked_a__f(mark(X)) ; } { Marked_mark(f(X)) > Marked_mark(X) ; } { Marked_mark(g(X)) > Marked_a__g(mark(X)) ; } { Marked_mark(g(X)) > Marked_mark(X) ; } { Marked_mark(s(X)) > Marked_mark(X) ; } { Marked_mark(sel(X1,X2)) > Marked_a__sel(mark(X1),mark(X2)) ; } { Marked_mark(sel(X1,X2)) > Marked_mark(X1) ; } { Marked_mark(sel(X1,X2)) > Marked_mark(X2) ; } } === 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 : 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 : 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 : 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: { mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(f(X)) >= a__f(mark(X)) ; mark(g(X)) >= a__g(mark(X)) ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(sel(X1,X2)) >= a__sel(mark(X1),mark(X2)) ; a__f(X) >= cons(mark(X),f(g(X))) ; a__f(X) >= f(X) ; a__g(s(X)) >= s(s(a__g(mark(X)))) ; a__g(0) >= s(0) ; a__g(X) >= g(X) ; a__sel(s(X),cons(Y,Z)) >= a__sel(mark(X),mark(Z)) ; a__sel(0,cons(X,Y)) >= mark(X) ; a__sel(X1,X2) >= sel(X1,X2) ; Marked_a__sel(s(X),cons(Y,Z)) > Marked_a__sel(mark(X),mark(Z)) ; Marked_a__sel(s(X),cons(Y,Z)) > Marked_mark(X) ; Marked_a__sel(s(X),cons(Y,Z)) > Marked_mark(Z) ; Marked_a__sel(0,cons(X,Y)) > Marked_mark(X) ; Marked_a__g(s(X)) > Marked_a__g(mark(X)) ; Marked_a__g(s(X)) > Marked_mark(X) ; Marked_a__f(X) > Marked_mark(X) ; Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; Marked_mark(f(X)) >= Marked_a__f(mark(X)) ; Marked_mark(f(X)) > Marked_mark(X) ; Marked_mark(g(X)) >= Marked_a__g(mark(X)) ; Marked_mark(g(X)) > Marked_mark(X) ; Marked_mark(s(X)) > Marked_mark(X) ; Marked_mark(sel(X1,X2)) >= Marked_a__sel(mark(X1),mark(X2)) ; Marked_mark(sel(X1,X2)) > Marked_mark(X1) ; Marked_mark(sel(X1,X2)) > Marked_mark(X2) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { mark(cons(X1,X2)) >= cons(mark(X1),X2) ; mark(f(X)) >= a__f(mark(X)) ; mark(g(X)) >= a__g(mark(X)) ; mark(s(X)) >= s(mark(X)) ; mark(0) >= 0 ; mark(sel(X1,X2)) >= a__sel(mark(X1),mark(X2)) ; a__f(X) >= cons(mark(X),f(g(X))) ; a__f(X) >= f(X) ; a__g(s(X)) >= s(s(a__g(mark(X)))) ; a__g(0) >= s(0) ; a__g(X) >= g(X) ; a__sel(s(X),cons(Y,Z)) >= a__sel(mark(X),mark(Z)) ; a__sel(0,cons(X,Y)) >= mark(X) ; a__sel(X1,X2) >= sel(X1,X2) ; Marked_a__sel(s(X),cons(Y,Z)) > Marked_a__sel(mark(X),mark(Z)) ; Marked_a__sel(s(X),cons(Y,Z)) > Marked_mark(X) ; Marked_a__sel(s(X),cons(Y,Z)) > Marked_mark(Z) ; Marked_a__sel(0,cons(X,Y)) > Marked_mark(X) ; Marked_a__g(s(X)) > Marked_a__g(mark(X)) ; Marked_a__g(s(X)) > Marked_mark(X) ; Marked_a__f(X) > Marked_mark(X) ; Marked_mark(cons(X1,X2)) > Marked_mark(X1) ; Marked_mark(f(X)) >= Marked_a__f(mark(X)) ; Marked_mark(f(X)) > Marked_mark(X) ; Marked_mark(g(X)) >= Marked_a__g(mark(X)) ; Marked_mark(g(X)) > Marked_mark(X) ; Marked_mark(s(X)) > Marked_mark(X) ; Marked_mark(sel(X1,X2)) >= Marked_a__sel(mark(X1),mark(X2)) ; Marked_mark(sel(X1,X2)) > Marked_mark(X1) ; Marked_mark(sel(X1,X2)) > Marked_mark(X2) ; } + 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.(549 bt (556) [333]) === 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 9.178443 seconds (real time) Cime Exit Status: 0