/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

** BEGIN proof argument **
All the DP problems were proved finite.
As all the involved DP processors are sound,
the TRS under analysis terminates.
** END proof argument **

** BEGIN proof description **
## Searching for a generalized rewrite rule
(a rule whose right-hand side contains a variable
that does not occur in the left-hand side)...
No generalized rewrite rule found!

## Applying the DP framework...
## 3 initial DP problems to solve.
## First, we try to decompose these problems into smaller problems.
## Round 1 [3 DP problems]:
  ## DP problem:
  Dependency pairs = [f^#(s(_0),s(_1),_2,_3) -> f^#(s(_0),minus(_1,_0),_2,_3), f^#(s(_0),0,_1,_2) -> f^#(_0,_2,minus(_1,s(_0)),_2), f^#(s(_0),s(_1),_2,_3) -> f^#(_0,_3,_2,_3)]
  TRS = {minus(0,_0) -> 0, minus(s(_0),0) -> s(_0), minus(s(_0),s(_1)) -> minus(_0,_1), le(0,_0) -> true, le(s(_0),0) -> false, le(s(_0),s(_1)) -> le(_0,_1), if(true,_0,_1) -> _0, if(false,_0,_1) -> _1, perfectp(0) -> false, perfectp(s(_0)) -> f(_0,s(0),s(_0),s(_0)), f(0,_0,0,_1) -> true, f(0,_0,s(_1),_2) -> false, f(s(_0),0,_1,_2) -> f(_0,_2,minus(_1,s(_0)),_2), f(s(_0),s(_1),_2,_3) -> if(le(_0,_1),f(s(_0),minus(_1,_0),_2,_3),f(_0,_3,_2,_3))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... This DP problem is too complex! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using
      the argument filtering:
      {s:[0], perfectp:[0], le:[0, 1], if:[0, 1, 2], minus:[0], f:[0, 1, 2, 3], f^#:[0, 1, 2, 3]}
      and the  precedence:
      s > [minus, 0, false, true], perfectp > [minus, s, if, le, 0, false, true, f], 0 > [true, false], f^# > [minus], f > [minus, if, le]
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [le^#(s(_0),s(_1)) -> le^#(_0,_1)]
  TRS = {minus(0,_0) -> 0, minus(s(_0),0) -> s(_0), minus(s(_0),s(_1)) -> minus(_0,_1), le(0,_0) -> true, le(s(_0),0) -> false, le(s(_0),s(_1)) -> le(_0,_1), if(true,_0,_1) -> _0, if(false,_0,_1) -> _1, perfectp(0) -> false, perfectp(s(_0)) -> f(_0,s(0),s(_0),s(_0)), f(0,_0,0,_1) -> true, f(0,_0,s(_1),_2) -> false, f(s(_0),0,_1,_2) -> f(_0,_2,minus(_1,s(_0)),_2), f(s(_0),s(_1),_2,_3) -> if(le(_0,_1),f(s(_0),minus(_1,_0),_2,_3),f(_0,_3,_2,_3))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [minus^#(s(_0),s(_1)) -> minus^#(_0,_1)]
  TRS = {minus(0,_0) -> 0, minus(s(_0),0) -> s(_0), minus(s(_0),s(_1)) -> minus(_0,_1), le(0,_0) -> true, le(s(_0),0) -> false, le(s(_0),s(_1)) -> le(_0,_1), if(true,_0,_1) -> _0, if(false,_0,_1) -> _1, perfectp(0) -> false, perfectp(s(_0)) -> f(_0,s(0),s(_0),s(_0)), f(0,_0,0,_1) -> true, f(0,_0,s(_1),_2) -> false, f(s(_0),0,_1,_2) -> f(_0,_2,minus(_1,s(_0)),_2), f(s(_0),s(_1),_2,_3) -> if(le(_0,_1),f(s(_0),minus(_1,_0),_2,_3),f(_0,_3,_2,_3))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
## All the DP problems were proved finite.
As all the involved DP processors are sound,
the TRS under analysis terminates.
Proof run on Linux version 3.10.0-1160.25.1.el7.x86_64 for amd64
using Java version 1.8.0_292
** END proof description **
Total number of generated unfolded rules = 0