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


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NO

** BEGIN proof argument **
The following rule was generated while unfolding the analyzed TRS:
[iteration = 6] f(b,b) -> f(b,b)
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {}.
We have r|p = f(b,b) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = f(b,b) loops w.r.t. the analyzed TRS.
** 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 = [h^#(_0) -> g^#(_0,_0), f^#(_0,_0) -> h^#(a), g^#(a,_0) -> f^#(b,activate(_0))]
  TRS = {h(_0) -> g(_0,_0), g(a,_0) -> f(b,activate(_0)), f(_0,_0) -> h(a), a -> b, activate(_0) -> _0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders... Failed!
    ## Trying with Knuth-Bendix orders... Failed!
  Don't know whether this DP problem is finite.
## A DP problem could not be proved finite.
## Now, we try to prove that this problem is infinite.
    ## Trying to find a loop (forward=true, backward=false, max=-1)
      # max_depth=2, unfold_variables=false:
        # Iteration 0: no loop found, 3 unfolded rules generated.
        # Iteration 1: no loop found, 5 unfolded rules generated.
        # Iteration 2: no loop found, 7 unfolded rules generated.
        # Iteration 3: no loop found, 9 unfolded rules generated.
        # Iteration 4: no loop found, 1 unfolded rule generated.
        # Iteration 5: no loop found, 2 unfolded rules generated.
        # Iteration 6: success, found a loop, 1 unfolded rule generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = f^#(_0,_0) -> h^#(a) [trans] is in U_IR^0.
        D = h^#(_0) -> g^#(_0,_0) is a dependency pair of IR.
        We build a composed triple from L0 and D.
        ==> L1 = f^#(_0,_0) -> g^#(a,a) [trans] is in U_IR^1.
        D = g^#(a,_0) -> f^#(b,activate(_0)) is a dependency pair of IR.
        We build a composed triple from L1 and D.
        ==> L2 = f^#(_0,_0) -> f^#(b,activate(a)) [trans] is in U_IR^2.
        We build a unit triple from L2.
        ==> L3 = f^#(_0,_0) -> f^#(b,activate(a)) [unit] is in U_IR^3.
        Let p3 = [0].
        The subterm at position p3 in the left-hand side of the rule of L3 unifies with
        the subterm at position p3 in the right-hand side of the rule of L3.
        ==> L4 = f^#(b,b) -> f^#(b,activate(a)) [unit] is in U_IR^4.
        Let p4 = [1].
        We unfold the rule of L4 forwards at position p4
        with the rule activate(_0) -> _0.
        ==> L5 = f^#(b,b) -> f^#(b,a) [unit] is in U_IR^5.
        Let p5 = [1].
        We unfold the rule of L5 forwards at position p5
        with the rule a -> b.
        ==> L6 = f^#(b,b) -> f^#(b,b) [unit] is in U_IR^6.
  This DP problem is infinite.
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 = 118