- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] h(x,c(y,z)) -> h(c(s(y),x),z) [2] h(c(s(x),c(s(0),y)),z) -> h(y,c(s(0),c(x,z))) 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: { h(c(s(x),c(s(0),y)),z) >= h(y,c(s(0),c(x,z))) ; h(x,c(y,z)) >= h(c(s(y),x),z) ; Marked_h(c(s(x),c(s(0),y)),z) >= Marked_h(y,c(s(0),c(x,z))) ; Marked_h(x,c(y,z)) >= Marked_h(c(s(y),x),z) ; } + Disjunctions:{ { Marked_h(c(s(x),c(s(0),y)),z) > Marked_h(y,c(s(0),c(x,z))) ; } { Marked_h(x,c(y,z)) > Marked_h(c(s(y),x),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 === 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 : 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: h(c(s(x),c(s(0),y)),z) >= h(y,c(s(0),c(x,z))) constraint: h(x,c(y,z)) >= h(c(s(y),x),z) constraint: Marked_h(c(s(x),c(s(0),y)),z) >= Marked_h(y,c(s(0),c(x,z))) constraint: Marked_h(x,c(y,z)) >= Marked_h(c(s(y),x),z) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_h -> 2 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] h(x,c(y,z)) -> h(c(s(y),x),z) [2] h(c(s(x),c(s(0),y)),z) -> h(y,c(s(0),c(x,z))) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ h ] (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 ] ]; [ Marked_h ] (X0,X1) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ s ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ c ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] [ 1 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ 0 ] () = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} Cime worked for 4.096346 seconds (real time) Cime Exit Status: 0