/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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...
## 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 = [app^#(app(app(compose,_0),_1),_2) -> app^#(_1,app(_0,_2)), app^#(app(app(compose,_0),_1),_2) -> app^#(_0,_2), app^#(reverse,_0) -> app^#(app(reverse2,_0),nil), app^#(app(reverse2,app(app(cons,_0),_1)),_2) -> app^#(app(reverse2,_1),app(app(cons,_0),_2)), app^#(app(reverse2,app(app(cons,_0),_1)),_2) -> app^#(app(cons,_0),_2)]
  TRS = {app(app(app(compose,_0),_1),_2) -> app(_1,app(_0,_2)), app(reverse,_0) -> app(app(reverse2,_0),nil), app(app(reverse2,nil),_0) -> _0, app(app(reverse2,app(app(cons,_0),_1)),_2) -> app(app(reverse2,_1),app(app(cons,_0),_2)), app(hd,app(app(cons,_0),_1)) -> _0, app(tl,app(app(cons,_0),_1)) -> _1, last -> app(app(compose,hd),reverse), init -> app(app(compose,reverse),app(app(compose,tl),reverse))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
    Successfully decomposed the DP problem into 1 smaller problem to solve!
## Round 2 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [app^#(app(app(compose,_0),_1),_2) -> app^#(_0,_2), app^#(app(app(compose,_0),_1),_2) -> app^#(_1,app(_0,_2)), app^#(app(reverse2,app(app(cons,_0),_1)),_2) -> app^#(app(reverse2,_1),app(app(cons,_0),_2)), app^#(app(reverse2,app(app(cons,_0),_1)),_2) -> app^#(app(cons,_0),_2)]
  TRS = {app(app(app(compose,_0),_1),_2) -> app(_1,app(_0,_2)), app(reverse,_0) -> app(app(reverse2,_0),nil), app(app(reverse2,nil),_0) -> _0, app(app(reverse2,app(app(cons,_0),_1)),_2) -> app(app(reverse2,_1),app(app(cons,_0),_2)), app(hd,app(app(cons,_0),_1)) -> _0, app(tl,app(app(cons,_0),_1)) -> _1, last -> app(app(compose,hd),reverse), init -> app(app(compose,reverse),app(app(compose,tl),reverse))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
    Successfully decomposed the DP problem into 1 smaller problem to solve!
## Round 3 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [app^#(app(app(compose,_0),_1),_2) -> app^#(_0,_2), app^#(app(app(compose,_0),_1),_2) -> app^#(_1,app(_0,_2)), app^#(app(reverse2,app(app(cons,_0),_1)),_2) -> app^#(app(reverse2,_1),app(app(cons,_0),_2))]
  TRS = {app(app(app(compose,_0),_1),_2) -> app(_1,app(_0,_2)), app(reverse,_0) -> app(app(reverse2,_0),nil), app(app(reverse2,nil),_0) -> _0, app(app(reverse2,app(app(cons,_0),_1)),_2) -> app(app(reverse2,_1),app(app(cons,_0),_2)), app(hd,app(app(cons,_0),_1)) -> _0, app(tl,app(app(cons,_0),_1)) -> _1, last -> app(app(compose,hd),reverse), init -> app(app(compose,reverse),app(app(compose,tl),reverse))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
    Successfully decomposed the DP problem into 1 smaller problem to solve!
## Round 4 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [app^#(app(app(compose,_0),_1),_2) -> app^#(_0,_2), app^#(app(app(compose,_0),_1),_2) -> app^#(_1,app(_0,_2))]
  TRS = {app(app(app(compose,_0),_1),_2) -> app(_1,app(_0,_2)), app(reverse,_0) -> app(app(reverse2,_0),nil), app(app(reverse2,nil),_0) -> _0, app(app(reverse2,app(app(cons,_0),_1)),_2) -> app(app(reverse2,_1),app(app(cons,_0),_2)), app(hd,app(app(cons,_0),_1)) -> _0, app(tl,app(app(cons,_0),_1)) -> _1, last -> app(app(compose,hd),reverse), init -> app(app(compose,reverse),app(app(compose,tl),reverse))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {compose:[1], cons:[0], last:[1], init:[2], nil:[0], reverse:[0], hd:[0], app(_0,_1):[_0 + _1], reverse2:[0], tl:[0], app^#(_0,_1):[_0]}
      for all instantiations of the variables with values greater than or equal to mu = 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