3.44/1.86 YES 3.44/1.86 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 3.44/1.86 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.44/1.86 3.44/1.86 3.44/1.86 Termination of the given RelTRS could be proven: 3.44/1.86 3.44/1.86 (0) RelTRS 3.44/1.86 (1) RelTRSRRRProof [EQUIVALENT, 35 ms] 3.44/1.86 (2) RelTRS 3.44/1.86 (3) RIsEmptyProof [EQUIVALENT, 0 ms] 3.44/1.86 (4) YES 3.44/1.86 3.44/1.86 3.44/1.86 ---------------------------------------- 3.44/1.86 3.44/1.86 (0) 3.44/1.86 Obligation: 3.44/1.86 Relative term rewrite system: 3.44/1.86 The relative TRS consists of the following R rules: 3.44/1.86 3.44/1.86 T(I(x), y) -> T(x, y) 3.44/1.86 3.44/1.86 The relative TRS consists of the following S rules: 3.44/1.86 3.44/1.86 T(x, y) -> T(x, I(y)) 3.44/1.86 3.44/1.86 3.44/1.86 ---------------------------------------- 3.44/1.86 3.44/1.86 (1) RelTRSRRRProof (EQUIVALENT) 3.44/1.86 We used the following monotonic ordering for rule removal: 3.44/1.86 Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : 3.44/1.86 3.44/1.86 <<< 3.44/1.86 POL(T(x_1, x_2)) = [[1], [0]] + [[1, 1], [1, 1]] * x_1 + [[1, 0], [1, 0]] * x_2 3.44/1.86 >>> 3.44/1.86 3.44/1.86 <<< 3.44/1.86 POL(I(x_1)) = [[0], [1]] + [[1, 0], [0, 1]] * x_1 3.44/1.86 >>> 3.44/1.86 3.44/1.86 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 3.44/1.86 Rules from R: 3.44/1.86 3.44/1.86 T(I(x), y) -> T(x, y) 3.44/1.86 Rules from S: 3.44/1.86 none 3.44/1.86 3.44/1.86 3.44/1.86 3.44/1.86 3.44/1.86 ---------------------------------------- 3.44/1.86 3.44/1.86 (2) 3.44/1.86 Obligation: 3.44/1.86 Relative term rewrite system: 3.44/1.86 R is empty. 3.44/1.86 The relative TRS consists of the following S rules: 3.44/1.86 3.44/1.86 T(x, y) -> T(x, I(y)) 3.44/1.86 3.44/1.86 3.44/1.86 ---------------------------------------- 3.44/1.86 3.44/1.86 (3) RIsEmptyProof (EQUIVALENT) 3.44/1.86 The TRS R is empty. Hence, termination is trivially proven. 3.44/1.86 ---------------------------------------- 3.44/1.86 3.44/1.86 (4) 3.44/1.86 YES 3.83/1.89 EOF