/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] a__f(_0,_0) -> a__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 = {_0->b}.
We have r|p = a__f(b,b) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = a__f(_0,_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 = [a__h^#(_0) -> a__g^#(mark(_0),_0), a__f^#(_0,_0) -> a__h^#(a__a), mark^#(f(_0,_1)) -> a__f^#(mark(_0),_1), a__g^#(a,_0) -> a__f^#(b,_0), mark^#(g(_0,_1)) -> a__g^#(mark(_0),_1), a__h^#(_0) -> mark^#(_0), mark^#(h(_0)) -> a__h^#(mark(_0)), mark^#(h(_0)) -> mark^#(_0), mark^#(g(_0,_1)) -> mark^#(_0), mark^#(f(_0,_1)) -> mark^#(_0)]
  TRS = {a__h(_0) -> a__g(mark(_0),_0), a__g(a,_0) -> a__f(b,_0), a__f(_0,_0) -> a__h(a__a), a__a -> b, mark(h(_0)) -> a__h(mark(_0)), mark(g(_0,_1)) -> a__g(mark(_0),_1), mark(a) -> a__a, mark(f(_0,_1)) -> a__f(mark(_0),_1), mark(b) -> b, a__h(_0) -> h(_0), a__g(_0,_1) -> g(_0,_1), a__a -> a, a__f(_0,_1) -> f(_0,_1)}
    ## 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=false, max=-1)
      # max_depth=2, unfold_variables=false:
        # Iteration 0: no loop found, 10 unfolded rules generated.
        # Iteration 1: no loop found, 39 unfolded rules generated.
        # Iteration 2: no loop found, 62 unfolded rules generated.
        # Iteration 3: no loop found, 80 unfolded rules generated.
        # Iteration 4: no loop found, 89 unfolded rules generated.
        # Iteration 5: no loop found, 97 unfolded rules generated.
        # Iteration 6: success, found a loop, 5 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = a__f^#(_0,_0) -> a__h^#(a__a) [trans] is in U_IR^0.
        D = a__h^#(_0) -> a__g^#(mark(_0),_0) is a dependency pair of IR.
        We build a composed triple from L0 and D.
        ==> L1 = a__f^#(_0,_0) -> a__g^#(mark(a__a),a__a) [trans] is in U_IR^1.
        D = a__g^#(a,_0) -> a__f^#(b,_0) is a dependency pair of IR.
        We build a composed triple from L1 and D.
        ==> L2 = [a__f^#(_0,_0) -> a__g^#(mark(a__a),a__a), a__g^#(a,_1) -> a__f^#(b,_1)] [comp] is in U_IR^2.
        Let p2 = [0, 0].
        We unfold the first rule of L2 forwards at position p2
        with the rule a__a -> a.
        ==> L3 = [a__f^#(_0,_0) -> a__g^#(mark(a),a__a), a__g^#(a,_1) -> a__f^#(b,_1)] [comp] is in U_IR^3.
        Let p3 = [0].
        We unfold the first rule of L3 forwards at position p3
        with the rule mark(a) -> a__a.
        ==> L4 = [a__f^#(_0,_0) -> a__g^#(a__a,a__a), a__g^#(a,_1) -> a__f^#(b,_1)] [comp] is in U_IR^4.
        Let p4 = [0].
        We unfold the first rule of L4 forwards at position p4
        with the rule a__a -> a.
        ==> L5 = [a__f^#(_0,_0) -> a__g^#(a,a__a), a__g^#(a,_1) -> a__f^#(b,_1)] [comp] is in U_IR^5.
        Let p5 = [1].
        We unfold the first rule of L5 forwards at position p5
        with the rule a__a -> b.
        ==> L6 = a__f^#(_0,_0) -> a__f^#(b,b) [trans] 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 = 1477