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TRS Context Sensitive pair #516978855
details
property
value
status
complete
benchmark
ex5.4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n007.star.cs.uiowa.edu
space
Transformed_outermost_08
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.04702687263 seconds
cpu usage
5.527752302
max memory
4.78208E8
stage attributes
key
value
output-size
8187
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 103 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 10 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 0 ms] (6) CSR (7) CSRRRRProof [EQUIVALENT, 0 ms] (8) CSR (9) CSRRRRProof [EQUIVALENT, 0 ms] (10) CSR (11) RisEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: *top*_0(f_1(f_0(g_1(x)))) -> *top*_0(x) f_0(f_1(f_0(g_1(x)))) -> f_0(x) g_0(f_1(f_0(g_1(x)))) -> g_1(x) *top*_0(f_0(f_1(f_0(g_0(x))))) -> *top*_0(f_0(x)) f_0(f_0(f_1(f_0(g_0(x))))) -> f_1(f_0(x)) g_0(f_0(f_1(f_0(g_0(x))))) -> g_0(f_0(x)) f_1(f_0(g_0(x))) -> x *top*_0(f_1(f_0(g_0(x)))) -> *top*_0(x) f_0(f_1(f_0(g_0(x)))) -> f_1(x) g_0(f_1(f_0(g_0(x)))) -> g_0(x) *top*_0(g_1(b_0)) -> *top*_0(f_0(g_1(b_0))) f_0(g_1(b_0)) -> f_1(f_0(g_1(b_0))) g_0(g_1(b_0)) -> g_0(f_0(g_1(b_0))) The replacement map contains the following entries: *top*_0: {1} f_1: empty set f_0: {1} g_1: empty set g_0: {1} b_0: empty set ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: *top*_0(f_1(f_0(g_1(x)))) -> *top*_0(x) f_0(f_1(f_0(g_1(x)))) -> f_0(x) g_0(f_1(f_0(g_1(x)))) -> g_1(x) *top*_0(f_0(f_1(f_0(g_0(x))))) -> *top*_0(f_0(x)) f_0(f_0(f_1(f_0(g_0(x))))) -> f_1(f_0(x)) g_0(f_0(f_1(f_0(g_0(x))))) -> g_0(f_0(x)) f_1(f_0(g_0(x))) -> x *top*_0(f_1(f_0(g_0(x)))) -> *top*_0(x) f_0(f_1(f_0(g_0(x)))) -> f_1(x) g_0(f_1(f_0(g_0(x)))) -> g_0(x) *top*_0(g_1(b_0)) -> *top*_0(f_0(g_1(b_0))) f_0(g_1(b_0)) -> f_1(f_0(g_1(b_0))) g_0(g_1(b_0)) -> g_0(f_0(g_1(b_0))) The replacement map contains the following entries: *top*_0: {1} f_1: empty set f_0: {1} g_1: empty set g_0: {1} b_0: empty set Used ordering: Polynomial interpretation [POLO]: POL(*top*_0(x_1)) = 2*x_1 POL(b_0) = 0 POL(f_0(x_1)) = 2*x_1 POL(f_1(x_1)) = x_1 POL(g_0(x_1)) = 2 + x_1 POL(g_1(x_1)) = 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g_0(f_1(f_0(g_1(x)))) -> g_1(x) *top*_0(f_0(f_1(f_0(g_0(x))))) -> *top*_0(f_0(x)) f_0(f_0(f_1(f_0(g_0(x))))) -> f_1(f_0(x))
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