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SRS Relat 19260 pair #381725302
details
property
value
status
complete
benchmark
rel09.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n039.star.cs.uiowa.edu
space
Zantema_06_relative
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
7.97170615196 seconds
cpu usage
27.561950889
max memory
2.52737536E9
stage attributes
key
value
output-size
5010
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRS Reverse [EQUIVALENT, 0 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 143 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 630 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 0 ms] (8) RelTRS (9) RIsEmptyProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: b(q(b(x1))) -> b(p(b(x1))) The relative TRS consists of the following S rules: 0(p(0(x1))) -> q(x1) 1(p(1(x1))) -> q(x1) 0(q(0(x1))) -> q(x1) 1(q(1(x1))) -> q(x1) p(x1) -> 1(p(1(0(1(x1))))) ---------------------------------------- (1) RelTRS Reverse (EQUIVALENT) We have reversed the following relative TRS [REVERSE]: The set of rules R is b(q(b(x1))) -> b(p(b(x1))) The set of rules S is 0(p(0(x1))) -> q(x1) 1(p(1(x1))) -> q(x1) 0(q(0(x1))) -> q(x1) 1(q(1(x1))) -> q(x1) p(x1) -> 1(p(1(0(1(x1))))) We have obtained the following relative TRS: The set of rules R is b(q(b(x1))) -> b(p(b(x1))) The set of rules S is 0(p(0(x1))) -> q(x1) 1(p(1(x1))) -> q(x1) 0(q(0(x1))) -> q(x1) 1(q(1(x1))) -> q(x1) p(x1) -> 1(0(1(p(1(x1))))) ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: b(q(b(x1))) -> b(p(b(x1))) The relative TRS consists of the following S rules: 0(p(0(x1))) -> q(x1) 1(p(1(x1))) -> q(x1) 0(q(0(x1))) -> q(x1) 1(q(1(x1))) -> q(x1) p(x1) -> 1(0(1(p(1(x1))))) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(b(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 >>> <<< POL(q(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1
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