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TRS Inner 89993 pair #381733449
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
n087.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.74814295769 seconds
cpu usage
3.886945766
max memory
1.97206016E8
stage attributes
key
value
output-size
6497
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QReductionProof [EQUIVALENT, 0 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QReductionProof [EQUIVALENT, 0 ms] (16) QDP (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, c(x), c(y)) -> f(y, y, f(y, x, y)) f(s(x), y, z) -> f(x, s(c(y)), c(z)) f(c(x), x, y) -> c(y) g(x, y) -> x g(x, y) -> y The set Q consists of the following terms: f(x0, c(x0), c(x1)) f(s(x0), x1, x2) f(c(x0), x0, x1) g(x0, x1) ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: F(x, c(x), c(y)) -> F(y, y, f(y, x, y)) F(x, c(x), c(y)) -> F(y, x, y) F(s(x), y, z) -> F(x, s(c(y)), c(z)) The TRS R consists of the following rules: f(x, c(x), c(y)) -> f(y, y, f(y, x, y)) f(s(x), y, z) -> f(x, s(c(y)), c(z)) f(c(x), x, y) -> c(y) g(x, y) -> x g(x, y) -> y The set Q consists of the following terms: f(x0, c(x0), c(x1)) f(s(x0), x1, x2) f(c(x0), x0, x1) g(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Q DP problem:
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