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TRS Standard pair #516967825
details
property
value
status
complete
benchmark
list-sum-prod-bin-assoc.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n054.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.35076904297 seconds
cpu usage
6.203283311
max memory
4.82500608E8
stage attributes
key
value
output-size
11517
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0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) MRRProof [EQUIVALENT, 3 ms] (9) QDP (10) PisEmptyProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QDPSizeChangeProof [EQUIVALENT, 0 ms] (16) YES (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) UsableRulesProof [EQUIVALENT, 0 ms] (22) QDP (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 0(#) -> # +(x, #) -> x +(#, x) -> x +(0(x), 0(y)) -> 0(+(x, y)) +(0(x), 1(y)) -> 1(+(x, y)) +(1(x), 0(y)) -> 1(+(x, y)) +(1(x), 1(y)) -> 0(+(+(x, y), 1(#))) +(+(x, y), z) -> +(x, +(y, z)) *(#, x) -> # *(0(x), y) -> 0(*(x, y)) *(1(x), y) -> +(0(*(x, y)), y) *(*(x, y), z) -> *(x, *(y, z)) sum(nil) -> 0(#) sum(cons(x, l)) -> +(x, sum(l)) prod(nil) -> 1(#) prod(cons(x, l)) -> *(x, prod(l)) 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: +^1(0(x), 0(y)) -> 0^1(+(x, y)) +^1(0(x), 0(y)) -> +^1(x, y) +^1(0(x), 1(y)) -> +^1(x, y) +^1(1(x), 0(y)) -> +^1(x, y) +^1(1(x), 1(y)) -> 0^1(+(+(x, y), 1(#))) +^1(1(x), 1(y)) -> +^1(+(x, y), 1(#)) +^1(1(x), 1(y)) -> +^1(x, y) +^1(+(x, y), z) -> +^1(x, +(y, z)) +^1(+(x, y), z) -> +^1(y, z) *^1(0(x), y) -> 0^1(*(x, y)) *^1(0(x), y) -> *^1(x, y) *^1(1(x), y) -> +^1(0(*(x, y)), y) *^1(1(x), y) -> 0^1(*(x, y)) *^1(1(x), y) -> *^1(x, y) *^1(*(x, y), z) -> *^1(x, *(y, z)) *^1(*(x, y), z) -> *^1(y, z) SUM(nil) -> 0^1(#) SUM(cons(x, l)) -> +^1(x, sum(l)) SUM(cons(x, l)) -> SUM(l) PROD(cons(x, l)) -> *^1(x, prod(l)) PROD(cons(x, l)) -> PROD(l) The TRS R consists of the following rules:
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