- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] minus(x,0) -> x [2] minus(s(x),s(y)) -> minus(x,y) [3] quot(0,s(y)) -> 0 [4] quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) [5] plus(0,y) -> y [6] plus(s(x),y) -> s(plus(x,y)) [7] plus(minus(x,s(0)),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0))) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> } { --> } { --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(s(x),s(y)) >= minus(x,y) ; minus(x,0) >= x ; quot(0,s(y)) >= 0 ; quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ; plus(minus(x,s(0)),minus(y,s(s(z)))) >= plus(minus(y,s(s(z))),minus(x,s(0))) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(x,y)) ; Marked_quot(s(x),s(y)) >= Marked_quot(minus(x,y),s(y)) ; } + Disjunctions:{ { Marked_quot(s(x),s(y)) > Marked_quot(minus(x,y),s(y)) ; } } === 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(s(x),s(y)) >= minus(x,y) constraint: minus(x,0) >= x constraint: quot(0,s(y)) >= 0 constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) constraint: plus(minus(x,s(0)),minus(y,s(s(z)))) >= plus(minus(y,s(s(z))), minus(x,s(0))) constraint: plus(0,y) >= y constraint: plus(s(x),y) >= s(plus(x,y)) constraint: Marked_quot(s(x),s(y)) >= Marked_quot(minus(x,y),s(y)) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(s(x),s(y)) >= minus(x,y) ; minus(x,0) >= x ; quot(0,s(y)) >= 0 ; quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ; plus(minus(x,s(0)),minus(y,s(s(z)))) >= plus(minus(y,s(s(z))),minus(x,s(0))) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(x,y)) ; Marked_minus(s(x),s(y)) >= Marked_minus(x,y) ; } + Disjunctions:{ { Marked_minus(s(x),s(y)) > Marked_minus(x,y) ; } } === 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(s(x),s(y)) >= minus(x,y) constraint: minus(x,0) >= x constraint: quot(0,s(y)) >= 0 constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) constraint: plus(minus(x,s(0)),minus(y,s(s(z)))) >= plus(minus(y,s(s(z))), minus(x,s(0))) constraint: plus(0,y) >= y constraint: plus(s(x),y) >= s(plus(x,y)) constraint: Marked_minus(s(x),s(y)) >= Marked_minus(x,y) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(s(x),s(y)) >= minus(x,y) ; minus(x,0) >= x ; quot(0,s(y)) >= 0 ; quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ; plus(minus(x,s(0)),minus(y,s(s(z)))) >= plus(minus(y,s(s(z))),minus(x,s(0))) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(x,y)) ; Marked_plus(minus(x,s(0)),minus(y,s(s(z)))) >= Marked_plus(minus(y,s(s(z))), minus(x,s(0))) ; Marked_plus(s(x),y) >= Marked_plus(x,y) ; } + Disjunctions:{ { Marked_plus(minus(x,s(0)),minus(y,s(s(z)))) > Marked_plus(minus(y,s(s(z))), minus(x,s(0))) ; } { Marked_plus(s(x),y) > Marked_plus(x,y) ; } } === 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(s(x),s(y)) >= minus(x,y) constraint: minus(x,0) >= x constraint: quot(0,s(y)) >= 0 constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) constraint: plus(minus(x,s(0)),minus(y,s(s(z)))) >= plus(minus(y,s(s(z))), minus(x,s(0))) constraint: plus(0,y) >= y constraint: plus(s(x),y) >= s(plus(x,y)) constraint: Marked_plus(minus(x,s(0)),minus(y,s(s(z)))) >= Marked_plus( minus(y,s(s(z))), minus(x,s(0))) constraint: Marked_plus(s(x),y) >= Marked_plus(x,y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(s(x),s(y)) >= minus(x,y) ; minus(x,0) >= x ; quot(0,s(y)) >= 0 ; quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) ; plus(minus(x,s(0)),minus(y,s(s(z)))) >= plus(minus(y,s(s(z))),minus(x,s(0))) ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(x,y)) ; Marked_plus(minus(x,s(0)),minus(y,s(s(z)))) >= Marked_plus(minus(y,s(s(z))), minus(x,s(0))) ; } + Disjunctions:{ { Marked_plus(minus(x,s(0)),minus(y,s(s(z)))) > Marked_plus(minus(y,s(s(z))), minus(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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: minus(s(x),s(y)) >= minus(x,y) constraint: minus(x,0) >= x constraint: quot(0,s(y)) >= 0 constraint: quot(s(x),s(y)) >= s(quot(minus(x,y),s(y))) constraint: plus(minus(x,s(0)),minus(y,s(s(z)))) >= plus(minus(y,s(s(z))), minus(x,s(0))) constraint: plus(0,y) >= y constraint: plus(s(x),y) >= s(plus(x,y)) constraint: Marked_plus(minus(x,s(0)),minus(y,s(s(z)))) >= Marked_plus( minus(y,s(s(z))), minus(x,s(0))) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] minus(x,0) -> x [2] minus(s(x),s(y)) -> minus(x,y) [3] quot(0,s(y)) -> 0 [4] quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) [5] plus(0,y) -> y [6] plus(s(x),y) -> s(plus(x,y)) [7] plus(minus(x,s(0)),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ minus ] (X0,X1) = 1 + 1*X0 + 0; [ plus ] (X0,X1) = 2*X0 + 2*X1 + 0; [ s ] (X0) = 2 + 1*X0 + 0; [ Marked_quot ] (X0,X1) = 2*X0 + 0; [ 0 ] () = 2 + 0; [ quot ] (X0,X1) = 2*X0 + 2*X1 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ minus ] (X0,X1) = 1*X0 + 0; [ plus ] (X0,X1) = 1*X0 + 1*X1 + 0; [ s ] (X0) = 2 + 1*X0 + 0; [ 0 ] () = 0; [ quot ] (X0,X1) = 1*X0 + 0; [ Marked_minus ] (X0,X1) = 1*X0 + 0; ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ minus ] (X0,X1) = 1*X0; [ plus ] (X0,X1) = 2*X1 + 2*X0 + 3; [ s ] (X0) = 1*X0 + 1; [ 0 ] () = 0; [ Marked_plus ] (X0,X1) = 2*X1 + 2*X0; [ quot ] (X0,X1) = 2*X0; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ minus ] (X0,X1) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 1 , 0 , 1 ] [ 0 , 1 , 0 ] [ 1 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ plus ] (X0,X1) = [ [ 1 , 0 , 1 ] [ 0 , 1 , 0 ] [ 1 , 0 , 1 ] ]*X1 + [ [ 1 , 0 , 1 ] [ 0 , 1 , 0 ] [ 1 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ s ] (X0) = [ [ 0 , 0 , 1 ] [ 0 , 1 , 0 ] [ 1 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ 0 ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_plus ] (X0,X1) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ quot ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; ]} ]} ]} ]} ]} Cime worked for 2.352587 seconds (real time) Cime Exit Status: 0