/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(mark(a__c),b,a__c) -> a__f(mark(a__c),b,a__c)
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 = a__f(mark(a__c),b,a__c) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = a__f(mark(a__c),b,a__c) 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__f^#(a,b,_0) -> a__f^#(mark(_0),_0,mark(_0)), mark^#(f(_0,_1,_2)) -> a__f^#(mark(_0),_1,mark(_2)), mark^#(f(_0,_1,_2)) -> mark^#(_0), mark^#(f(_0,_1,_2)) -> mark^#(_2), a__f^#(a,b,_0) -> mark^#(_0), a__f^#(a,b,_0) -> mark^#(_0)]
  TRS = {a__f(a,b,_0) -> a__f(mark(_0),_0,mark(_0)), a__c -> a, a__c -> b, mark(f(_0,_1,_2)) -> a__f(mark(_0),_1,mark(_2)), mark(c) -> a__c, mark(a) -> a, mark(b) -> b, a__f(_0,_1,_2) -> f(_0,_1,_2), a__c -> c}
    ## 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, 6 unfolded rules generated.
        # Iteration 1: no loop found, 26 unfolded rules generated.
        # Iteration 2: no loop found, 95 unfolded rules generated.
        # Iteration 3: no loop found, 386 unfolded rules generated.
        # Iteration 4: no loop found, 1666 unfolded rules generated.
        # Iteration 5: no loop found, 7165 unfolded rules generated.
        # Iteration 6: success, found a loop, 525 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = a__f^#(a,b,_0) -> a__f^#(mark(_0),_0,mark(_0)) [trans] is in U_IR^0.
        We build a unit triple from L0.
        ==> L1 = a__f^#(a,b,_0) -> a__f^#(mark(_0),_0,mark(_0)) [unit] is in U_IR^1.
        Let p1 = [0].
        We unfold the rule of L1 backwards at position p1
        with the rule mark(a) -> a.
        ==> L2 = a__f^#(mark(a),b,_0) -> a__f^#(mark(_0),_0,mark(_0)) [unit] is in U_IR^2.
        Let p2 = [0, 0].
        We unfold the rule of L2 backwards at position p2
        with the rule a__c -> a.
        ==> L3 = a__f^#(mark(a__c),b,a__c) -> a__f^#(mark(a__c),a__c,mark(a__c)) [unit] is in U_IR^3.
        Let p3 = [1].
        We unfold the rule of L3 forwards at position p3
        with the rule a__c -> b.
        ==> L4 = a__f^#(mark(a__c),b,a__c) -> a__f^#(mark(a__c),b,mark(a__c)) [unit] is in U_IR^4.
        Let p4 = [2, 0].
        We unfold the rule of L4 forwards at position p4
        with the rule a__c -> c.
        ==> L5 = a__f^#(mark(a__c),b,a__c) -> a__f^#(mark(a__c),b,mark(c)) [unit] is in U_IR^5.
        Let p5 = [2].
        We unfold the rule of L5 forwards at position p5
        with the rule mark(c) -> a__c.
        ==> L6 = a__f^#(mark(a__c),b,a__c) -> a__f^#(mark(a__c),b,a__c) [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 = 17979