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TRS Stand 20472 pair #381710795
details
property
value
status
complete
benchmark
thiemann05.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n190.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.61927509308 seconds
cpu usage
7.028664453
max memory
4.4218368E8
stage attributes
key
value
output-size
19356
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 10 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QReductionProof [EQUIVALENT, 0 ms] (18) QDP (19) TransformationProof [EQUIVALENT, 3 ms] (20) QDP (21) DependencyGraphProof [EQUIVALENT, 0 ms] (22) QDP (23) TransformationProof [EQUIVALENT, 0 ms] (24) QDP (25) TransformationProof [EQUIVALENT, 0 ms] (26) QDP (27) TransformationProof [EQUIVALENT, 0 ms] (28) QDP (29) QDPOrderProof [EQUIVALENT, 41 ms] (30) QDP (31) DependencyGraphProof [EQUIVALENT, 0 ms] (32) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: isLeaf(leaf) -> true isLeaf(cons(u, v)) -> false left(cons(u, v)) -> u right(cons(u, v)) -> v concat(leaf, y) -> y concat(cons(u, v), y) -> cons(u, concat(v, y)) less_leaves(u, v) -> if1(isLeaf(u), isLeaf(v), u, v) if1(b, true, u, v) -> false if1(b, false, u, v) -> if2(b, u, v) if2(true, u, v) -> true if2(false, u, v) -> less_leaves(concat(left(u), right(u)), concat(left(v), right(v))) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: isLeaf(leaf) -> true isLeaf(cons(u, v)) -> false left(cons(u, v)) -> u right(cons(u, v)) -> v concat(leaf, y) -> y concat(cons(u, v), y) -> cons(u, concat(v, y)) less_leaves(u, v) -> if1(isLeaf(u), isLeaf(v), u, v) if1(b, true, u, v) -> false if1(b, false, u, v) -> if2(b, u, v) if2(true, u, v) -> true if2(false, u, v) -> less_leaves(concat(left(u), right(u)), concat(left(v), right(v))) The set Q consists of the following terms: isLeaf(leaf) isLeaf(cons(x0, x1)) left(cons(x0, x1)) right(cons(x0, x1)) concat(leaf, x0) concat(cons(x0, x1), x2)
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