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TRS Relat 75837 pair #381724966
details
property
value
status
complete
benchmark
rt2-4.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
Relative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.80504989624 seconds
cpu usage
4.370916952
max memory
3.49229056E8
stage attributes
key
value
output-size
2410
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRS Reverse [SOUND, 0 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 29 ms] (4) RelTRS (5) RIsEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: f(g(x)) -> x The relative TRS consists of the following S rules: a -> h(g(f(a))) ---------------------------------------- (1) RelTRS Reverse (SOUND) We have reversed the following relative TRS [REVERSE]: The set of rules R is f(g(x)) -> x The set of rules S is a -> h(g(f(a))) We have obtained the following relative TRS: The set of rules R is g(f(x)) -> x The set of rules S is a'(x) -> a'(f(g(h(x)))) ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: g(f(x)) -> x The relative TRS consists of the following S rules: a'(x) -> a'(f(g(h(x)))) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(g(x_1)) = [[0], [0]] + [[1, 1], [0, 2]] * x_1 >>> <<< POL(f(x_1)) = [[0], [1]] + [[1, 0], [0, 1]] * x_1 >>> <<< POL(a'(x_1)) = [[2], [2]] + [[1, 0], [0, 0]] * x_1 >>> <<< POL(h(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: g(f(x)) -> x Rules from S: none
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