/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


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...
## 1 initial DP problem to solve.
## First, we try to decompose this problem into smaller problems.
## Round 1 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [+^#(_0,c(_1,_2)) -> c^#(_1,+(_0,_2)), +^#(_0,c(_1,_2)) -> +^#(_0,_2), +^#(c(_0,_1),_2) -> +^#(_1,_2), c^#(_0,c(_1,_2)) -> +^#(_0,_1), c^#(_0,c(_1,_2)) -> c^#(+(_0,_1),_2), +^#(c(_0,_1),_2) -> c^#(_0,+(_1,_2))]
  TRS = {+(0,0) -> 0, +(0,1) -> 1, +(0,2) -> 2, +(0,3) -> 3, +(0,4) -> 4, +(0,5) -> 5, +(0,6) -> 6, +(0,7) -> 7, +(0,8) -> 8, +(0,9) -> 9, +(1,0) -> 1, +(1,1) -> 2, +(1,2) -> 3, +(1,3) -> 4, +(1,4) -> 5, +(1,5) -> 6, +(1,6) -> 7, +(1,7) -> 8, +(1,8) -> 9, +(1,9) -> c(1,0), +(2,0) -> 2, +(2,1) -> 3, +(2,2) -> 4, +(2,3) -> 5, +(2,4) -> 6, +(2,5) -> 7, +(2,6) -> 8, +(2,7) -> 9, +(2,8) -> c(1,0), +(2,9) -> c(1,1), +(3,0) -> 3, +(3,1) -> 4, +(3,2) -> 5, +(3,3) -> 6, +(3,4) -> 7, +(3,5) -> 8, +(3,6) -> 9, +(3,7) -> c(1,0), +(3,8) -> c(1,1), +(3,9) -> c(1,2), +(4,0) -> 4, +(4,1) -> 5, +(4,2) -> 6, +(4,3) -> 7, +(4,4) -> 8, +(4,5) -> 9, +(4,6) -> c(1,0), +(4,7) -> c(1,1), +(4,8) -> c(1,2), +(4,9) -> c(1,3), +(5,0) -> 5, +(5,1) -> 6, +(5,2) -> 7, +(5,3) -> 8, +(5,4) -> 9, +(5,5) -> c(1,0), +(5,6) -> c(1,1), +(5,7) -> c(1,2), +(5,8) -> c(1,3), +(5,9) -> c(1,4), +(6,0) -> 6, +(6,1) -> 7, +(6,2) -> 8, +(6,3) -> 9, +(6,4) -> c(1,0), +(6,5) -> c(1,1), +(6,6) -> c(1,2), +(6,7) -> c(1,3), +(6,8) -> c(1,4), +(6,9) -> c(1,5), +(7,0) -> 7, +(7,1) -> 8, +(7,2) -> 9, +(7,3) -> c(1,0), +(7,4) -> c(1,1), +(7,5) -> c(1,2), +(7,6) -> c(1,3), +(7,7) -> c(1,4), +(7,8) -> c(1,5), +(7,9) -> c(1,6), +(8,0) -> 8, +(8,1) -> 9, +(8,2) -> c(1,0), +(8,3) -> c(1,1), +(8,4) -> c(1,2), +(8,5) -> c(1,3), +(8,6) -> c(1,4), +(8,7) -> c(1,5), +(8,8) -> c(1,6), +(8,9) -> c(1,7), +(9,0) -> 9, +(9,1) -> c(1,0), +(9,2) -> c(1,1), +(9,3) -> c(1,2), +(9,4) -> c(1,3), +(9,5) -> c(1,4), +(9,6) -> c(1,5), +(9,7) -> c(1,6), +(9,8) -> c(1,7), +(9,9) -> c(1,8), +(_0,c(_1,_2)) -> c(_1,+(_0,_2)), +(c(_0,_1),_2) -> c(_0,+(_1,_2)), c(0,_0) -> _0, c(_0,c(_1,_2)) -> c(+(_0,_1),_2)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... This DP problem is too complex! Aborting!
    ## Trying with lexicographic path orders... Failed!
    ## Trying with Knuth-Bendix orders...
      The constraints are satisfied by the Knuth-Bendix order using
      the precedence:
      + > [5, c, 6, 7, 8]
      and the weight function:
      {variables:1, 5:2, 4:1, 1:1, c:1, 3:1, 9:2, 0:1, 6:2, 7:2, +:0, 2:1, 8:2, c^#:0, +^#:0}
  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