- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] i(x,x) -> i(a,b) [2] g(x,x) -> g(a,b) [3] h(s(f(x))) -> h(f(x)) [4] f(s(x)) -> s(s(f(h(s(x))))) [5] f(g(s(x),y)) -> f(g(x,s(y))) [6] h(g(x,s(y))) -> h(g(s(x),y)) [7] h(i(x,y)) -> i(i(c,h(h(y))),x) [8] g(a,g(x,g(b,g(a,g(x,y))))) -> g(a,g(a,g(a,g(x,g(b,g(b,y)))))) 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: { i(x,x) >= i(a,b) ; g(a,g(x,g(b,g(a,g(x,y))))) >= g(a,g(a,g(a,g(x,g(b,g(b,y)))))) ; g(x,x) >= g(a,b) ; h(i(x,y)) >= i(i(c,h(h(y))),x) ; h(g(x,s(y))) >= h(g(s(x),y)) ; h(s(f(x))) >= h(f(x)) ; f(g(s(x),y)) >= f(g(x,s(y))) ; f(s(x)) >= s(s(f(h(s(x))))) ; Marked_f(g(s(x),y)) >= Marked_f(g(x,s(y))) ; Marked_f(s(x)) >= Marked_f(h(s(x))) ; } + Disjunctions:{ { Marked_f(g(s(x),y)) > Marked_f(g(x,s(y))) ; } { Marked_f(s(x)) > Marked_f(h(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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: i(x,x) >= i(a,b) constraint: g(a,g(x,g(b,g(a,g(x,y))))) >= g(a,g(a,g(a,g(x,g(b,g(b,y)))))) constraint: g(x,x) >= g(a,b) constraint: h(i(x,y)) >= i(i(c,h(h(y))),x) constraint: h(g(x,s(y))) >= h(g(s(x),y)) constraint: h(s(f(x))) >= h(f(x)) constraint: f(g(s(x),y)) >= f(g(x,s(y))) constraint: f(s(x)) >= s(s(f(h(s(x))))) constraint: Marked_f(g(s(x),y)) >= Marked_f(g(x,s(y))) constraint: Marked_f(s(x)) >= Marked_f(h(s(x))) APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { i(x,x) >= i(a,b) ; g(a,g(x,g(b,g(a,g(x,y))))) >= g(a,g(a,g(a,g(x,g(b,g(b,y)))))) ; g(x,x) >= g(a,b) ; h(i(x,y)) >= i(i(c,h(h(y))),x) ; h(g(x,s(y))) >= h(g(s(x),y)) ; h(s(f(x))) >= h(f(x)) ; f(g(s(x),y)) >= f(g(x,s(y))) ; f(s(x)) >= s(s(f(h(s(x))))) ; Marked_h(i(x,y)) >= Marked_h(h(y)) ; Marked_h(i(x,y)) >= Marked_h(y) ; Marked_h(g(x,s(y))) >= Marked_h(g(s(x),y)) ; Marked_h(s(f(x))) >= Marked_h(f(x)) ; } + Disjunctions:{ { Marked_h(i(x,y)) > Marked_h(h(y)) ; } { Marked_h(i(x,y)) > Marked_h(y) ; } { Marked_h(g(x,s(y))) > Marked_h(g(s(x),y)) ; } { Marked_h(s(f(x))) > Marked_h(f(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 : 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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: i(x,x) >= i(a,b) constraint: g(a,g(x,g(b,g(a,g(x,y))))) >= g(a,g(a,g(a,g(x,g(b,g(b,y)))))) constraint: g(x,x) >= g(a,b) constraint: h(i(x,y)) >= i(i(c,h(h(y))),x) constraint: h(g(x,s(y))) >= h(g(s(x),y)) constraint: h(s(f(x))) >= h(f(x)) constraint: f(g(s(x),y)) >= f(g(x,s(y))) constraint: f(s(x)) >= s(s(f(h(s(x))))) constraint: Marked_h(i(x,y)) >= Marked_h(h(y)) constraint: Marked_h(i(x,y)) >= Marked_h(y) constraint: Marked_h(g(x,s(y))) >= Marked_h(g(s(x),y)) constraint: Marked_h(s(f(x))) >= Marked_h(f(x)) APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { i(x,x) >= i(a,b) ; g(a,g(x,g(b,g(a,g(x,y))))) >= g(a,g(a,g(a,g(x,g(b,g(b,y)))))) ; g(x,x) >= g(a,b) ; h(i(x,y)) >= i(i(c,h(h(y))),x) ; h(g(x,s(y))) >= h(g(s(x),y)) ; h(s(f(x))) >= h(f(x)) ; f(g(s(x),y)) >= f(g(x,s(y))) ; f(s(x)) >= s(s(f(h(s(x))))) ; Marked_i(x,x) >= Marked_i(a,b) ; } + Disjunctions:{ { Marked_i(x,x) > Marked_i(a,b) ; } } === 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: { i(x,x) >= i(a,b) ; g(a,g(x,g(b,g(a,g(x,y))))) >= g(a,g(a,g(a,g(x,g(b,g(b,y)))))) ; g(x,x) >= g(a,b) ; h(i(x,y)) >= i(i(c,h(h(y))),x) ; h(g(x,s(y))) >= h(g(s(x),y)) ; h(s(f(x))) >= h(f(x)) ; f(g(s(x),y)) >= f(g(x,s(y))) ; f(s(x)) >= s(s(f(h(s(x))))) ; Marked_i(x,x) > Marked_i(a,b) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { i(x,x) >= i(a,b) ; g(a,g(x,g(b,g(a,g(x,y))))) >= g(a,g(a,g(a,g(x,g(b,g(b,y)))))) ; g(x,x) >= g(a,b) ; h(i(x,y)) >= i(i(c,h(h(y))),x) ; h(g(x,s(y))) >= h(g(s(x),y)) ; h(s(f(x))) >= h(f(x)) ; f(g(s(x),y)) >= f(g(x,s(y))) ; f(s(x)) >= s(s(f(h(s(x))))) ; Marked_i(x,x) > Marked_i(a,b) ; } + 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.(309 bt (132) [36]) === 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 40.003699 seconds (real time) Cime Exit Status: 0