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TRS Standard pair #516960855
details
property
value
status
complete
benchmark
thiemann17.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n064.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.97528004646 seconds
cpu usage
8.147774843
max memory
5.69761792E8
stage attributes
key
value
output-size
13894
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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) UsableRulesReductionPairsProof [EQUIVALENT, 9 ms] (13) QDP (14) PisEmptyProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPOrderProof [EQUIVALENT, 79 ms] (22) QDP (23) DependencyGraphProof [EQUIVALENT, 0 ms] (24) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y)) sum(cons(0, x), y) -> sum(x, y) sum(nil, y) -> y empty(nil) -> true empty(cons(n, x)) -> false tail(nil) -> nil tail(cons(n, x)) -> x head(cons(n, x)) -> n weight(x) -> if(empty(x), empty(tail(x)), x) if(true, b, x) -> weight_undefined_error if(false, b, x) -> if2(b, x) if2(true, x) -> head(x) if2(false, x) -> weight(sum(x, cons(0, tail(tail(x))))) 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: sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y)) sum(cons(0, x), y) -> sum(x, y) sum(nil, y) -> y empty(nil) -> true empty(cons(n, x)) -> false tail(nil) -> nil tail(cons(n, x)) -> x head(cons(n, x)) -> n weight(x) -> if(empty(x), empty(tail(x)), x) if(true, b, x) -> weight_undefined_error if(false, b, x) -> if2(b, x) if2(true, x) -> head(x) if2(false, x) -> weight(sum(x, cons(0, tail(tail(x))))) The set Q consists of the following terms: sum(cons(s(x0), x1), cons(x2, x3)) sum(cons(0, x0), x1) sum(nil, x0) empty(nil) empty(cons(x0, x1)) tail(nil) tail(cons(x0, x1)) head(cons(x0, x1)) weight(x0) if(true, x0, x1)
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