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TRS Conditional pair #487562996
details
property
value
status
complete
benchmark
ohl.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n077.star.cs.uiowa.edu
space
Mixed_CTRS_2014
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.97680592537 seconds
cpu usage
4.13379642
max memory
2.92446208E8
stage attributes
key
value
output-size
3997
starexec-result
MAYBE
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Quasi decreasingness of the given CTRS could not be shown: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) QDP (7) NonTerminationLoopProof [COMPLETE, 0 ms] (8) NO ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: h(d) -> c(a) h(d) -> c(b) f(k(a), k(b), x) -> f(x, x, x) The conditional TRS C consists of the following conditional rules: g(x) -> k(y) <= h(x) -> d, h(x) -> c(y) ---------------------------------------- (1) CTRSToQTRSProof (SOUND) The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(x) -> U1(h(x), x) U1(d, x) -> U2(h(x)) U2(c(y)) -> k(y) h(d) -> c(a) h(d) -> c(b) f(k(a), k(b), x) -> f(x, x, x) Q is empty. ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: G(x) -> U1^1(h(x), x) G(x) -> H(x) U1^1(d, x) -> U2^1(h(x)) U1^1(d, x) -> H(x) F(k(a), k(b), x) -> F(x, x, x) The TRS R consists of the following rules: g(x) -> U1(h(x), x) U1(d, x) -> U2(h(x)) U2(c(y)) -> k(y) h(d) -> c(a) h(d) -> c(b) f(k(a), k(b), x) -> f(x, x, x) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: F(k(a), k(b), x) -> F(x, x, x)
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