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TRS Equat 89423 pair #381732797
details
property
value
status
complete
benchmark
BAG_nosorts-noand.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n075.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.4634449482 seconds
cpu usage
6.125676909
max memory
3.34303232E8
stage attributes
key
value
output-size
23562
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 218 ms] (2) ETRS (3) RRRPoloETRSProof [EQUIVALENT, 104 ms] (4) ETRS (5) RRRPoloETRSProof [EQUIVALENT, 51 ms] (6) ETRS (7) RRRPoloETRSProof [EQUIVALENT, 41 ms] (8) ETRS (9) RRRPoloETRSProof [EQUIVALENT, 0 ms] (10) ETRS (11) RRRPoloETRSProof [EQUIVALENT, 16 ms] (12) ETRS (13) RisEmptyProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: union(X, empty) -> X union(empty, X) -> X 0(z) -> z U11(tt, X, Y) -> U12(tt, X, Y) U12(tt, X, Y) -> 0(mult(X, Y)) U21(tt, X, Y) -> U22(tt, X, Y) U22(tt, X, Y) -> plus(0(mult(X, Y)), Y) U31(tt, X, Y) -> U32(tt, X, Y) U32(tt, X, Y) -> 0(plus(X, Y)) U41(tt, X, Y) -> U42(tt, X, Y) U42(tt, X, Y) -> 1(plus(X, Y)) U51(tt, X, Y) -> U52(tt, X, Y) U52(tt, X, Y) -> 0(plus(plus(X, Y), 1(z))) U61(tt, A, B) -> U62(tt, A, B) U62(tt, A, B) -> mult(prod(A), prod(B)) U71(tt, A, B) -> U72(tt, A, B) U72(tt, A, B) -> plus(sum(A), sum(B)) mult(z, X) -> z mult(0(X), Y) -> U11(tt, X, Y) mult(1(X), Y) -> U21(tt, X, Y) plus(z, X) -> X plus(0(X), 0(Y)) -> U31(tt, X, Y) plus(0(X), 1(Y)) -> U41(tt, X, Y) plus(1(X), 1(Y)) -> U51(tt, X, Y) prod(empty) -> 1(z) prod(singl(X)) -> X prod(union(A, B)) -> U61(tt, A, B) sum(empty) -> 0(z) sum(singl(X)) -> X sum(union(A, B)) -> U71(tt, A, B) The set E consists of the following equations: mult(x, y) == mult(y, x) plus(x, y) == plus(y, x) union(x, y) == union(y, x) mult(mult(x, y), z') == mult(x, mult(y, z')) plus(plus(x, y), z') == plus(x, plus(y, z')) union(union(x, y), z') == union(x, union(y, z')) ---------------------------------------- (1) RRRPoloETRSProof (EQUIVALENT) The following E TRS is given: Equational rewrite system: The TRS R consists of the following rules: union(X, empty) -> X union(empty, X) -> X 0(z) -> z U11(tt, X, Y) -> U12(tt, X, Y) U12(tt, X, Y) -> 0(mult(X, Y)) U21(tt, X, Y) -> U22(tt, X, Y) U22(tt, X, Y) -> plus(0(mult(X, Y)), Y) U31(tt, X, Y) -> U32(tt, X, Y) U32(tt, X, Y) -> 0(plus(X, Y)) U41(tt, X, Y) -> U42(tt, X, Y) U42(tt, X, Y) -> 1(plus(X, Y)) U51(tt, X, Y) -> U52(tt, X, Y) U52(tt, X, Y) -> 0(plus(plus(X, Y), 1(z))) U61(tt, A, B) -> U62(tt, A, B) U62(tt, A, B) -> mult(prod(A), prod(B)) U71(tt, A, B) -> U72(tt, A, B)
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