/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(u(d,h(d),_0),k(b),u(d,h(d),_0)) -> f(u(d,h(d),_0),k(b),u(d,h(d),_0))
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(u(d,h(d),_0),k(b),u(d,h(d),_0)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = f(u(d,h(d),_0),k(b),u(d,h(d),_0)) 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 = [f^#(k(a),k(b),_0) -> f^#(_0,_0,_0)]
  TRS = {g(_0) -> u(h(_0),h(_0),_0), u(d,c(_0),_1) -> k(_0), h(d) -> c(a), h(d) -> c(b), f(k(a),k(b),_0) -> f(_0,_0,_0)}
    ## 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... 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=true, max=20)
      # max_depth=20, unfold_variables=false:
        # Iteration 0: no loop found, 1 unfolded rule generated.
        # Iteration 1: no loop found, 1 unfolded rule generated.
        # Iteration 2: no loop found, 2 unfolded rules generated.
        # Iteration 3: no loop found, 3 unfolded rules generated.
        # Iteration 4: no loop found, 2 unfolded rules generated.
        # Iteration 5: no loop found, 3 unfolded rules generated.
        # Iteration 6: success, found a loop, 2 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = f^#(k(a),k(b),_0) -> f^#(_0,_0,_0) [trans] is in U_IR^0.
        We build a unit triple from L0.
        ==> L1 = f^#(k(a),k(b),_0) -> f^#(_0,_0,_0) [unit] is in U_IR^1.
        Let p1 = [0].
        We unfold the rule of L1 backwards at position p1
        with the rule u(d,c(_0),_1) -> k(_0).
        ==> L2 = f^#(u(d,c(a),_0),k(b),_1) -> f^#(_1,_1,_1) [unit] is in U_IR^2.
        Let p2 = [0, 1].
        We unfold the rule of L2 backwards at position p2
        with the rule h(d) -> c(a).
        ==> L3 = f^#(u(d,h(d),_0),k(b),_1) -> f^#(_1,_1,_1) [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^#(u(d,h(d),_0),k(b),u(d,h(d),_0)) -> f^#(u(d,h(d),_0),u(d,h(d),_0),u(d,h(d),_0)) [unit] is in U_IR^4.
        Let p4 = [1, 1].
        We unfold the rule of L4 forwards at position p4
        with the rule h(d) -> c(b).
        ==> L5 = f^#(u(d,h(d),_0),k(b),u(d,h(d),_0)) -> f^#(u(d,h(d),_0),u(d,c(b),_0),u(d,h(d),_0)) [unit] is in U_IR^5.
        Let p5 = [1].
        We unfold the rule of L5 forwards at position p5
        with the rule u(d,c(_0),_1) -> k(_0).
        ==> L6 = f^#(u(d,h(d),_0),k(b),u(d,h(d),_0)) -> f^#(u(d,h(d),_0),k(b),u(d,h(d),_0)) [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 = 23