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TRS Standard pair #516966350
details
property
value
status
complete
benchmark
id_inc.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n167.star.cs.uiowa.edu
space
AProVE_08
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.71760702133 seconds
cpu usage
7.344596936
max memory
5.13847296E8
stage attributes
key
value
output-size
9427
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 24 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (12) QDP (13) QDPOrderProof [EQUIVALENT, 69 ms] (14) QDP (15) DependencyGraphProof [EQUIVALENT, 0 ms] (16) QDP (17) QDPOrderProof [EQUIVALENT, 0 ms] (18) QDP (19) PisEmptyProof [EQUIVALENT, 0 ms] (20) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(s(x)) -> f(id_inc(c(x, x))) f(c(s(x), y)) -> g(c(x, y)) g(c(s(x), y)) -> g(c(y, x)) g(c(x, s(y))) -> g(c(y, x)) g(c(x, x)) -> f(x) id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) id_inc(s(x)) -> s(id_inc(x)) id_inc(0) -> 0 id_inc(0) -> s(0) Q is empty. ---------------------------------------- (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(s(x)) -> F(id_inc(c(x, x))) F(s(x)) -> ID_INC(c(x, x)) F(c(s(x), y)) -> G(c(x, y)) G(c(s(x), y)) -> G(c(y, x)) G(c(x, s(y))) -> G(c(y, x)) G(c(x, x)) -> F(x) ID_INC(c(x, y)) -> ID_INC(x) ID_INC(c(x, y)) -> ID_INC(y) ID_INC(s(x)) -> ID_INC(x) The TRS R consists of the following rules: f(s(x)) -> f(id_inc(c(x, x))) f(c(s(x), y)) -> g(c(x, y)) g(c(s(x), y)) -> g(c(y, x)) g(c(x, s(y))) -> g(c(y, x)) g(c(x, x)) -> f(x) id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) id_inc(s(x)) -> s(id_inc(x)) id_inc(0) -> 0 id_inc(0) -> s(0) Q is empty. 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) ----------------------------------------
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