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TRS_Innermost 2019-03-28 22.12 pair #432271318
details
property
value
status
complete
benchmark
PEANO_complete_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.24684 seconds
cpu usage
5.78604
user time
5.52835
system time
0.257688
max virtual memory
1.8409116E7
max residence set size
352428.0
stage attributes
key
value
starexec-result
YES
output
5.66/2.19 YES 5.66/2.20 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 5.66/2.20 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.66/2.20 5.66/2.20 5.66/2.20 Termination w.r.t. Q of the given QTRS could be proven: 5.66/2.20 5.66/2.20 (0) QTRS 5.66/2.20 (1) QTRSToCSRProof [SOUND, 0 ms] 5.66/2.20 (2) CSR 5.66/2.20 (3) CSRRRRProof [EQUIVALENT, 32 ms] 5.66/2.20 (4) CSR 5.66/2.20 (5) CSRRRRProof [EQUIVALENT, 12 ms] 5.66/2.20 (6) CSR 5.66/2.20 (7) CSRRRRProof [EQUIVALENT, 0 ms] 5.66/2.20 (8) CSR 5.66/2.20 (9) CSRRRRProof [EQUIVALENT, 0 ms] 5.66/2.20 (10) CSR 5.66/2.20 (11) CSRRRRProof [EQUIVALENT, 0 ms] 5.66/2.20 (12) CSR 5.66/2.20 (13) CSRRRRProof [EQUIVALENT, 0 ms] 5.66/2.20 (14) CSR 5.66/2.20 (15) CSRRRRProof [EQUIVALENT, 0 ms] 5.66/2.20 (16) CSR 5.66/2.20 (17) CSRRRRProof [EQUIVALENT, 12 ms] 5.66/2.20 (18) CSR 5.66/2.20 (19) CSRRRRProof [EQUIVALENT, 0 ms] 5.66/2.20 (20) CSR 5.66/2.20 (21) CSRRRRProof [EQUIVALENT, 0 ms] 5.66/2.20 (22) CSR 5.66/2.20 (23) CSRRRRProof [EQUIVALENT, 0 ms] 5.66/2.20 (24) CSR 5.66/2.20 (25) RisEmptyProof [EQUIVALENT, 0 ms] 5.66/2.20 (26) YES 5.66/2.20 5.66/2.20 5.66/2.20 ---------------------------------------- 5.66/2.20 5.66/2.20 (0) 5.66/2.20 Obligation: 5.66/2.20 Q restricted rewrite system: 5.66/2.20 The TRS R consists of the following rules: 5.66/2.20 5.66/2.20 active(U11(tt, V1, V2)) -> mark(U12(isNat(V1), V2)) 5.66/2.20 active(U12(tt, V2)) -> mark(U13(isNat(V2))) 5.66/2.20 active(U13(tt)) -> mark(tt) 5.66/2.20 active(U21(tt, V1)) -> mark(U22(isNat(V1))) 5.66/2.20 active(U22(tt)) -> mark(tt) 5.66/2.20 active(U31(tt, N)) -> mark(N) 5.66/2.20 active(U41(tt, M, N)) -> mark(s(plus(N, M))) 5.66/2.20 active(and(tt, X)) -> mark(X) 5.66/2.20 active(isNat(0)) -> mark(tt) 5.66/2.20 active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2)) 5.66/2.20 active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) 5.66/2.20 active(isNatKind(0)) -> mark(tt) 5.66/2.20 active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2))) 5.66/2.20 active(isNatKind(s(V1))) -> mark(isNatKind(V1)) 5.66/2.20 active(plus(N, 0)) -> mark(U31(and(isNat(N), isNatKind(N)), N)) 5.66/2.20 active(plus(N, s(M))) -> mark(U41(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N)) 5.66/2.20 active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3) 5.66/2.20 active(U12(X1, X2)) -> U12(active(X1), X2) 5.66/2.20 active(U13(X)) -> U13(active(X)) 5.66/2.20 active(U21(X1, X2)) -> U21(active(X1), X2) 5.66/2.20 active(U22(X)) -> U22(active(X)) 5.66/2.20 active(U31(X1, X2)) -> U31(active(X1), X2) 5.66/2.20 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 5.66/2.20 active(s(X)) -> s(active(X)) 5.66/2.20 active(plus(X1, X2)) -> plus(active(X1), X2) 5.66/2.20 active(plus(X1, X2)) -> plus(X1, active(X2)) 5.66/2.20 active(and(X1, X2)) -> and(active(X1), X2) 5.66/2.20 U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3)) 5.66/2.20 U12(mark(X1), X2) -> mark(U12(X1, X2)) 5.66/2.20 U13(mark(X)) -> mark(U13(X)) 5.66/2.20 U21(mark(X1), X2) -> mark(U21(X1, X2)) 5.66/2.20 U22(mark(X)) -> mark(U22(X)) 5.66/2.20 U31(mark(X1), X2) -> mark(U31(X1, X2)) 5.66/2.20 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 5.66/2.20 s(mark(X)) -> mark(s(X)) 5.66/2.20 plus(mark(X1), X2) -> mark(plus(X1, X2)) 5.66/2.20 plus(X1, mark(X2)) -> mark(plus(X1, X2)) 5.66/2.20 and(mark(X1), X2) -> mark(and(X1, X2)) 5.66/2.20 proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3)) 5.66/2.20 proper(tt) -> ok(tt) 5.66/2.20 proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)) 5.66/2.20 proper(isNat(X)) -> isNat(proper(X)) 5.66/2.20 proper(U13(X)) -> U13(proper(X)) 5.66/2.20 proper(U21(X1, X2)) -> U21(proper(X1), proper(X2)) 5.66/2.20 proper(U22(X)) -> U22(proper(X)) 5.66/2.20 proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) 5.66/2.20 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 5.66/2.20 proper(s(X)) -> s(proper(X)) 5.66/2.20 proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) 5.66/2.20 proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 5.66/2.20 proper(0) -> ok(0) 5.66/2.20 proper(isNatKind(X)) -> isNatKind(proper(X)) 5.66/2.20 U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3)) 5.66/2.20 U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)) 5.66/2.20 isNat(ok(X)) -> ok(isNat(X)) 5.66/2.20 U13(ok(X)) -> ok(U13(X)) 5.66/2.20 U21(ok(X1), ok(X2)) -> ok(U21(X1, X2))
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