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TRS Standard pair #516967717
details
property
value
status
complete
benchmark
#4.19.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n059.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
NTI_22
configuration
default
runtime (wallclock)
0.42320394516 seconds
cpu usage
0.727999412
max memory
1.00077568E8
stage attributes
key
value
output-size
4665
starexec-result
NO
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- NO ** BEGIN proof argument ** The following rule was generated while unfolding the analyzed TRS: [iteration = 5] f(_0,c(_0),c(g(_1,c(_0)))) -> f(_1,c(_0),c(g(_1,c(_0)))) Let l be the left-hand side and r be the right-hand side of this rule. Let p = epsilon, theta1 = {_0->_1} and theta2 = {}. We have r|p = f(_1,c(_0),c(g(_1,c(_0)))) and theta2(theta1(l)) = theta1(r|p). Hence, the term theta1(l) = f(_1,c(_1),c(g(_1,c(_1)))) 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... ## 2 initial DP problems to solve. ## First, we try to decompose these problems into smaller problems. ## Round 1 [2 DP problems]: ## DP problem: Dependency pairs = [f^#(_0,c(_0),c(_1)) -> f^#(_1,_1,f(_1,_0,_1)), f^#(_0,c(_0),c(_1)) -> f^#(_1,_0,_1)] TRS = {f(_0,c(_0),c(_1)) -> f(_1,_1,f(_1,_0,_1)), f(s(_0),_1,_2) -> f(_0,s(c(_1)),c(_2)), f(c(_0),_0,_1) -> c(_1), g(_0,_1) -> _0, g(_0,_1) -> _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. ## DP problem: Dependency pairs = [f^#(s(_0),_1,_2) -> f^#(_0,s(c(_1)),c(_2))] TRS = {f(_0,c(_0),c(_1)) -> f(_1,_1,f(_1,_0,_1)), f(s(_0),_1,_2) -> f(_0,s(c(_1)),c(_2)), f(c(_0),_0,_1) -> c(_1), g(_0,_1) -> _0, g(_0,_1) -> _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. ## Some DP problems could not be proved finite. ## Now, we try to prove that one of these problems is infinite. ## Trying to find a loop (forward=true, backward=false, max=-1) # max_depth=3, unfold_variables=false: # Iteration 0: no loop found, 2 unfolded rules generated. # Iteration 1: no loop found, 4 unfolded rules generated. # Iteration 2: no loop found, 4 unfolded rules generated. # Iteration 3: no loop found, 2 unfolded rules generated. # Iteration 4: no loop found, 2 unfolded rules generated. # Iteration 5: no loop found, 0 unfolded rule generated. No loop found at all! # max_depth=3, unfold_variables=true: # Iteration 0: no loop found, 2 unfolded rules generated. # Iteration 1: no loop found, 4 unfolded rules generated. # Iteration 2: no loop found, 6 unfolded rules generated. # Iteration 3: no loop found, 10 unfolded rules generated. # Iteration 4: no loop found, 18 unfolded rules generated. # Iteration 5: success, found a loop, 11 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. L0 = f^#(_0,c(_0),c(_1)) -> f^#(_1,_1,f(_1,_0,_1)) [trans] is in U_IR^0. We build a unit triple from L0. ==> L1 = f^#(_0,c(_0),c(_1)) -> f^#(_1,_1,f(_1,_0,_1)) [unit] is in U_IR^1. Let p1 = [0]. We unfold the rule of L1 forwards at position p1 with the rule g(_0,_1) -> _0. ==> L2 = f^#(_0,c(_0),c(g(_1,_2))) -> f^#(_1,g(_1,_2),f(g(_1,_2),_0,g(_1,_2))) [unit] is in U_IR^2. Let p2 = [1]. We unfold the rule of L2 forwards at position p2 with the rule g(_0,_1) -> _1. ==> L3 = f^#(_0,c(_0),c(g(_1,_2))) -> f^#(_1,_2,f(g(_1,_2),_0,g(_1,_2))) [unit] is in U_IR^3. Let p3 = [2, 0]. We unfold the rule of L3 forwards at position p3 with the rule g(_0,_1) -> _1. ==> L4 = f^#(_0,c(_0),c(g(_1,_2))) -> f^#(_1,_2,f(_2,_0,g(_1,_2))) [unit] is in U_IR^4. Let p4 = [2]. We unfold the rule of L4 forwards at position p4 with the rule f(c(_0),_0,_1) -> c(_1). ==> L5 = f^#(_0,c(_0),c(g(_1,c(_0)))) -> f^#(_1,c(_0),c(g(_1,c(_0)))) [unit] is in U_IR^5. 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 = 468
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