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SRS Standard pair #516969130
details
property
value
status
complete
benchmark
pi.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
Waldmann_06_SRS
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
8.77028608322 seconds
cpu usage
31.322462086
max memory
1.337790464E9
stage attributes
key
value
output-size
20899
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 39 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 1 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 13 ms] (7) QDP (8) QDPOrderProof [EQUIVALENT, 147 ms] (9) QDP (10) DependencyGraphProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPOrderProof [EQUIVALENT, 309 ms] (13) QDP (14) DependencyGraphProof [EQUIVALENT, 0 ms] (15) QDP (16) QDPOrderProof [EQUIVALENT, 310 ms] (17) QDP (18) DependencyGraphProof [EQUIVALENT, 0 ms] (19) QDP (20) QDPOrderProof [EQUIVALENT, 12 ms] (21) QDP (22) DependencyGraphProof [EQUIVALENT, 0 ms] (23) QDP (24) QDPOrderProof [EQUIVALENT, 7 ms] (25) QDP (26) PisEmptyProof [EQUIVALENT, 0 ms] (27) YES (28) QDP (29) UsableRulesProof [EQUIVALENT, 0 ms] (30) QDP (31) QDPSizeChangeProof [EQUIVALENT, 0 ms] (32) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 3(1(x1)) -> 4(1(x1)) 5(9(x1)) -> 2(6(5(x1))) 3(5(x1)) -> 8(9(7(x1))) 9(x1) -> 3(2(3(x1))) 8(4(x1)) -> 6(x1) 2(6(x1)) -> 4(3(x1)) 3(8(x1)) -> 3(2(7(x1))) 9(x1) -> 5(0(2(x1))) 8(8(4(x1))) -> 1(9(x1)) 7(1(x1)) -> 6(9(x1)) 3(9(x1)) -> 9(3(x1)) 7(5(x1)) -> 1(0(x1)) 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: 5^1(9(x1)) -> 2^1(6(5(x1))) 5^1(9(x1)) -> 5^1(x1) 3^1(5(x1)) -> 8^1(9(7(x1))) 3^1(5(x1)) -> 9^1(7(x1)) 3^1(5(x1)) -> 7^1(x1) 9^1(x1) -> 3^1(2(3(x1))) 9^1(x1) -> 2^1(3(x1)) 9^1(x1) -> 3^1(x1) 2^1(6(x1)) -> 3^1(x1) 3^1(8(x1)) -> 3^1(2(7(x1))) 3^1(8(x1)) -> 2^1(7(x1)) 3^1(8(x1)) -> 7^1(x1) 9^1(x1) -> 5^1(0(2(x1))) 9^1(x1) -> 2^1(x1) 8^1(8(4(x1))) -> 9^1(x1) 7^1(1(x1)) -> 9^1(x1) 3^1(9(x1)) -> 9^1(3(x1)) 3^1(9(x1)) -> 3^1(x1)
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