- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] minus(x,0) -> x [2] minus(0,y) -> 0 [3] minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) [4] minus(x,plus(y,z)) -> minus(minus(x,y),z) [5] p(s(s(x))) -> s(p(s(x))) [6] p(0) -> s(s(0)) [7] div(s(x),s(y)) -> s(div(minus(x,y),s(y))) [8] div(plus(x,y),z) -> plus(div(x,z),div(y,z)) [9] plus(0,y) -> y [10] plus(s(x),y) -> s(plus(y,minus(s(x),s(0)))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 4 components: { --> --> --> --> --> --> --> --> --> } { --> } { --> --> --> --> --> --> --> --> --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(0,y) >= 0 ; minus(s(x),s(y)) >= minus(p(s(x)),p(s(y))) ; minus(x,0) >= x ; minus(x,plus(y,z)) >= minus(minus(x,y),z) ; p(0) >= s(s(0)) ; p(s(s(x))) >= s(p(s(x))) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(y,minus(s(x),s(0)))) ; div(s(x),s(y)) >= s(div(minus(x,y),s(y))) ; div(plus(x,y),z) >= plus(div(x,z),div(y,z)) ; Marked_div(s(x),s(y)) >= Marked_div(minus(x,y),s(y)) ; Marked_div(plus(x,y),z) >= Marked_div(x,z) ; Marked_div(plus(x,y),z) >= Marked_div(y,z) ; } + Disjunctions:{ { Marked_div(s(x),s(y)) > Marked_div(minus(x,y),s(y)) ; } { Marked_div(plus(x,y),z) > Marked_div(x,z) ; } { Marked_div(plus(x,y),z) > Marked_div(y,z) ; } } === 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: minus(0,y) >= 0 constraint: minus(s(x),s(y)) >= minus(p(s(x)),p(s(y))) constraint: minus(x,0) >= x constraint: minus(x,plus(y,z)) >= minus(minus(x,y),z) constraint: p(0) >= s(s(0)) constraint: p(s(s(x))) >= s(p(s(x))) constraint: plus(0,y) >= y constraint: plus(s(x),y) >= s(plus(y,minus(s(x),s(0)))) constraint: div(s(x),s(y)) >= s(div(minus(x,y),s(y))) constraint: div(plus(x,y),z) >= plus(div(x,z),div(y,z)) constraint: Marked_div(s(x),s(y)) >= Marked_div(minus(x,y),s(y)) constraint: Marked_div(plus(x,y),z) >= Marked_div(x,z) constraint: Marked_div(plus(x,y),z) >= Marked_div(y,z) APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(0,y) >= 0 ; minus(s(x),s(y)) >= minus(p(s(x)),p(s(y))) ; minus(x,0) >= x ; minus(x,plus(y,z)) >= minus(minus(x,y),z) ; p(0) >= s(s(0)) ; p(s(s(x))) >= s(p(s(x))) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(y,minus(s(x),s(0)))) ; div(s(x),s(y)) >= s(div(minus(x,y),s(y))) ; div(plus(x,y),z) >= plus(div(x,z),div(y,z)) ; Marked_plus(s(x),y) >= Marked_plus(y,minus(s(x),s(0))) ; } + Disjunctions:{ { Marked_plus(s(x),y) > Marked_plus(y,minus(s(x),s(0))) ; } } === 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: { minus(0,y) >= 0 ; minus(s(x),s(y)) >= minus(p(s(x)),p(s(y))) ; minus(x,0) >= x ; minus(x,plus(y,z)) >= minus(minus(x,y),z) ; p(0) >= s(s(0)) ; p(s(s(x))) >= s(p(s(x))) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(y,minus(s(x),s(0)))) ; div(s(x),s(y)) >= s(div(minus(x,y),s(y))) ; div(plus(x,y),z) >= plus(div(x,z),div(y,z)) ; Marked_plus(s(x),y) > Marked_plus(y,minus(s(x),s(0))) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { minus(0,y) >= 0 ; minus(s(x),s(y)) >= minus(p(s(x)),p(s(y))) ; minus(x,0) >= x ; minus(x,plus(y,z)) >= minus(minus(x,y),z) ; p(0) >= s(s(0)) ; p(s(s(x))) >= s(p(s(x))) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(y,minus(s(x),s(0)))) ; div(s(x),s(y)) >= s(div(minus(x,y),s(y))) ; div(plus(x,y),z) >= plus(div(x,z),div(y,z)) ; Marked_plus(s(x),y) > Marked_plus(y,minus(s(x),s(0))) ; } + 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.(148 bt (175) [21]) === 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 5.180794 seconds (real time) Cime Exit Status: 0