- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] p(0) -> 0 [2] p(s(x)) -> x [3] le(0,y) -> true [4] le(s(x),0) -> false [5] le(s(x),s(y)) -> le(x,y) [6] minus(x,0) -> x [7] minus(x,s(y)) -> if(le(x,s(y)),0,p(minus(x,p(s(y))))) [8] if(true,x,y) -> x [9] if(false,x,y) -> y Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { p(0) >= 0 ; p(s(x)) >= x ; le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; minus(x,0) >= x ; minus(x,s(y)) >= if(le(x,s(y)),0,p(minus(x,p(s(y))))) ; if(true,x,y) >= x ; if(false,x,y) >= y ; Marked_minus(x,s(y)) >= Marked_minus(x,p(s(y))) ; } + Disjunctions:{ { Marked_minus(x,s(y)) > Marked_minus(x,p(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 === 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: p(0) >= 0 constraint: p(s(x)) >= x constraint: le(0,y) >= true constraint: le(s(x),0) >= false constraint: le(s(x),s(y)) >= le(x,y) constraint: minus(x,0) >= x constraint: minus(x,s(y)) >= if(le(x,s(y)),0,p(minus(x,p(s(y))))) constraint: if(true,x,y) >= x constraint: if(false,x,y) >= y constraint: Marked_minus(x,s(y)) >= Marked_minus(x,p(s(y))) APPLY CRITERIA (Subterm criterion) ST: Marked_le -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] p(0) -> 0 [2] p(s(x)) -> x [3] le(0,y) -> true [4] le(s(x),0) -> false [5] le(s(x),s(y)) -> le(x,y) [6] minus(x,0) -> x [7] minus(x,s(y)) -> if(le(x,s(y)),0,p(minus(x,p(s(y))))) [8] if(true,x,y) -> x [9] if(false,x,y) -> y , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ 0 ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ le ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ s ] (X0) = [ [ 1 , 1 , 1 ] [ 0 , 0 , 0 ] [ 1 , 1 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; [ minus ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 1 , 0 , 0 ] [ 1 , 1 , 0 ] [ 1 , 0 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ p ] (X0) = [ [ 1 , 0 , 0 ] [ 1 , 0 , 0 ] [ 1 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_minus ] (X0,X1) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ false ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ true ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ if ] (X0,X1,X2) = [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X2 + [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} Cime worked for 3.080496 seconds (real time) Cime Exit Status: 0